Newsgroup sci.math.num-analysis 29183

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\documentclass[a4paper,12pt]{article}
\parindent 0pt  \parskip 5pt plus 3pt minus 1pt
\begin{document}
\title{\sf Post-doctoral position researching the\\
Low-dimensional modelling of fluid dynamics}
\author{Prof Tony Roberts\\
Dept Maths \& Computing\\ 
University of Southern Queensland\\
Toowoomba, Qld 4350\\
Australia\\
E-mail: \texttt{aroberts@usq.edu.au}}
\date{13 December, 1996}
\maketitle
\section*{The project} 
The issue to be addressed in this project is the creation of accurate, 
useful and complete mathematical models describing the behaviour of 
the flow of shallow water in an estuary, river or flood, and the 
creeping flow of thin viscous fluids such as paint.  In these examples 
there is potentially an enormous wealth of detail in a full physical 
simulation.  Such a level of detail makes it impossible to simulate in 
full, and thus tractable simple approximations are needed.  
Traditional methods may lead to error.  However, the recent 
development of centre manifold theory and associated techniques can 
put these simpler dynamical models on a firm basis and thereby create 
new and quantitatively accurate models.  The complete project proposal 
is available at 
\begin{center}
\texttt{http://www.sci.usq.edu.au/staff/robertsa/Mech/mech.html}
\end{center}
Candidates must possess a PhD, or have the equivalent experience.  
Their expertise must lie in both areas of modern dynamical systems 
theory and in fluid mechanics, preferably with experience in 
free-surface hydrodynamics.
\section*{The position}
The project is funded by a research grant from the Australian Research 
Council.  The appointment is to commence ASAP and will be offered for 
a limited term of up to three years, depending upon level and 
conditions.
The appointment will be made at Academic Level~A or Level~B depending 
upon expertise,  currently a {\em salary range\/} of 
A\$36,694--A\$43,042 per annum.
A selection will be made according to the following criteria:
\begin{itemize}
   \item  PhD, or equivalent, in a relevant area with a commitment to 
   high quality research;
   \item  expertise in both fluid mechanics and dynamical 
   systems, particularly free-surface hydrodynamics and centre manifolds;
   \item  communication skills;
   \item  energy and initiative;
\end{itemize}
although there will be a preference for Australian residents.  
Applicants should document, in their application, their demonstrated 
ability in the above categories.
Applicants should forward their application by {\bf 20~January, 1997} 
to Prof Tony Roberts (address given above).
\section*{Further information}
The department forms a vital part of a developing regional university 
and offers courses in Applied Mathematics, Statistics and Computer 
Science.  It has a large base of networked {\sc pc}s, teaching 
laboratories with both {\sc dos} and {\sc linux}, an undergraduate 
laboratory of \textsc{dec} alphas, a post-graduate workstation 
laboratory, and has access to supercomputers around Australia.  
Further information about the department, its research and courses is 
obtainable over the WWW via the home page
\begin{center}
   {\tt http://www.sci.usq.edu.au}
\end{center}
\end{document}
---------------------------------------------------------------------
Professor A.J. Roberts     
Dept of Mathematics & Computing     E-mail: aroberts@usq.edu.au
University of Southern Queensland   Phone:  (076) 312943
Toowoomba, Queensland 4350          Fax:    (076) 312721
AUSTRALIA                           WWW: http://www.sci.usq.edu.au
                                    /pub/MC/staff/robertsa/home.html
---------------------------------------------------------------------

        I'm trying to use a superquadric to interpolate 3D points, I tried the 
approach proposed by R.Bajcsy and F.Solina but i can't understand how they 
programmed their minimisation of their 11 parameters ( 3 rotation 3 
translation 5 superquadric parameters), they use a non linear minimization 
using least square method but the thing to minize is so hudge that i really 
don't know how they programmed it
I hope someone can help me 
Best regards
R.Blume

Hi Netters,
During my research I come up with a recurrence I don't know
how to tackle.
Here is the recurrence, using TeX-like notations :
\alpha u^{n+1} + \beta u^{n} + \gamma u^{n} u^{n+1} + \delta = 0,
where \alpha > 0 and \delta goes faster to zero than u^{n} possibly does.
The question is :
Are there any conditions on \alpha, \beta and \gamma which ensure
than u^{n} tends to zero whatever u^{0} is ?
Another related question is : 
Have you got any reference to books dealing with nonlinear recursions ?
Thanks for you help,
Fabrice.
     ************************************
     *                                  *
     *        veerse@cnrm.meteo.fr      *
     *         Tel: 05.61.07.84.69      *
     *         Fax: 05.61.07.84.53      *
     *          METEO FRANCE            *
     *        C.N.R.M / G.M.A.P         *
     * 	     42, Av. G. Coriolis        *
     *      31057 TOULOUSE CEDEX        *  
     *            FRANCE                *
     ************************************

Serge Goossens  wrote:
>What is the best way to evaluate (double precision IEEE compliant)
>sqrt(1-x*x) when x -> 0 ?  
I don't think you can do any better than this:
Do a taylor series expansion about zero
sqrt(1-x*x) = 1 - x^2/2 + x^4/8 - ...
and evaluate as many terms as you want, for x sufficiently small all
you need is
1 - x*x/2
If you want to try different numbers of terms, add then up starting
with the smallest.
Also think about what you are doing with sqrt(1-x*x), if for instance
you are doing something like
1 - sqrt(1-x*x) 
expand _that_ as x^2 *( 1 - x^2/8 + ...)
>Currently I am using: 
>sin( acos( x ) ) 
>Which can be trusted if acos() and sin() are evaluated accurately?
>What can one expect when using:
>sqrt(1+x) * sqrt(1-x)
>Using 1-x*x is of course not an option.
>How does MATLAB handle this?
>>> sin(acos(1.0e-8))
>ans =
>     1
>Thanks in advance.
>Best Regards.
>Serge
>-- 
>	     Short Course on Domain Decomposition Methods
>	       http://www.cs.kuleuven.ac.be/~serge/dd/
>--
>     Serge.Goossens@cs.kuleuven.ac.be        Department of Computer Science
>     http://www.cs.kuleuven.ac.be/~serge/    Katholieke Universiteit Leuven
>     Phone: +32 (0)16 327087                 Celestijnenlaan 200A
>     Fax:   +32 (0)16 327996                 B-3001 Heverlee        BELGIUM
===============================================================
  Andrew McLean                 !  Defence Research Agency
  Advanced Concepts Group       !  Winfrith Technology Centre
  Sonar Systems Department      !  Dorchester, Dorset DT2 8XJ
                                !  United Kingdom
  e-mail : almclean@dra.hmg.gb  !
   phone : +44 1305 212428      !  DRA is a division of DERA
     fax : +44 1305 212107      !  an Agency of the MOD

ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=2,t,m,l=1) <= b :
Date  : Fri Dec 13 05:27:37 1996
Author: U.Mutlu
Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 2 
l <= 1295           l  = 1 
v <= 255            v <= 54 
b <= 1679615        b <= 9999
Trivial cases are: t=m=k (ie. Complete Design), t=m=1, v=k, (b=1)
"+" means bonus nbr
Key to the signs at the end of the entry b:
 [.] Non-trivial Steiner System with L=1 (exact covering, packing, t-design)
 [*] Sch馬heim Lower Bound (SLB) or a known higher Exact Lower Bound (ELB)
met
\t/m        2/2        2/3        2/4        2/5        2/6        2/7
v\        1+/1+      1+/2+      1+/3+      1+/4+      1+/5+      1+/6+
----------------------------------------------------------------------
  2:        1 *        1 *        1 *        1 *        1 *        1 *
  3:        3 *        1 *        1 *        1 *        1 *        1 *
  4:        6 *        2 *        1 *        1 *        1 *        1 *
  5:       10 *        4 *        2 *        1 *        1 *        1 *
  6:       15 *        6          3 *        2 *        1 *        1 *
  7:       21 *        9          5          3 *        2 *        1 *
  8:       28 *       12          7          4          3          2 *
  9:       36 *       16          9          6          4          3  
 10:       45 *       20         12          8          5          4  
 11:       55 *       25         15         10          7          5  
 12:       66 *       30         18         12          9          6  
 13:       78 *       36         22         15         11          8  
 14:       91 *       42         26         18         13         10  
 15:      105 *       49         30         21         15         12  
 16:      120 *       56         35         24         18         14  
 17:      136 *       64         40         28         21         16  
 18:      153 *       72         45         32         24         18  
 19:      171 *       81         51         36         27         21  
 20:      190 *       90         57         40         30         24  
 21:      210 *      100         63         45         34         27  
 22:      231 *      110         70         50         38         30  
 23:      253 *      121         77         55         42         33  
 24:      276 *      132         84         60         46         36  
 25:      300 *      144         92         66         50         40  
 26:      325 *      156        100         72         55         44  
 27:      351 *      169        108         78         60         48  
 28:      378 *      182        117         84         65         52  
 29:      406 *      196        126         91         70         56  
 30:      435 *      210        135         98         75         60  
 31:      465 *      225        145        105         81         65  
 32:      496 *      240        155        112         87         70  
 33:      528 *      256        165        120         93         75  
 34:      561 *      272        176        128         99         80  
 35:      595 *      289        187        136        105         85  
 36:      630 *      306        198        144        112         90  
 37:      666 *      324        210        153        119         96  
 38:      703 *      342        222        162        126        102  
 39:      741 *      361        234        171        133        108  
 40:      780 *      380        247        180        140        114  
 41:      820 *      400        260        190        148        120  
 42:      861 *      420        273        200        156        126  
 43:      903 *      441        287        210        164        133  
 44:      946 *      462        301        220        172        140  
 45:      990 *      484        315        231        180        147  
 46:     1035 *      506        330        242        189        154  
 47:     1081 *      529        345        253        198        161  
 48:     1128 *      552        360        264        207        168  
 49:     1176 *      576        376        276        216        176  
 50:     1225 *      600        392        288        225        184  
 51:     1275 *      625        408        300        235        192  
 52:     1326 *      650        425        312        245        200  
 53:     1378 *      676        442        325        255        208  
 54:     1431 *      702        459        338        265        216  
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=3,t,m,l=1) <= b :
Date  : Fri Dec 13 05:27:37 1996
Author: U.Mutlu
Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 3 
l <= 1295           l  = 1 
v <= 255            v <= 54 
b <= 1679615        b <= 9999
Trivial cases are: t=m=k (ie. Complete Design), t=m=1, v=k, (b=1)
"+" means bonus nbr
Key to the signs at the end of the entry b:
 [.] Non-trivial Steiner System with L=1 (exact covering, packing, t-design)
 [*] Sch馬heim Lower Bound (SLB) or a known higher Exact Lower Bound (ELB)
met
\t/m        2/2        2/3        2/4        2/5        2/6        2/7
v\        1+/1+      1+/2+      1+/3+      1+/4+      1+/5+      1+/6+
----------------------------------------------------------------------
  3:        1 *        1 *        1 *        1 *        1 *        1 *
  4:        3 *        1 *        1 *        1 *        1 *        1 *
  5:        4 *        2 *        1 *        1 *        1 *        1 *
  6:        6 *        2 *        2 *        1 *        1 *        1 *
  7:        7.*        4          2 *        2 *        1 *        1 *
  8:       11 *        5          3          2 *        2 *        1 *
  9:       12.*        7          3 *        3          2 *        2 *
 10:       17 *        8          5          3          3          2 *
 11:       19 *       10          6          4          3          3  
 12:       24 *       11          8          4          4          3  
 13:       26.*       13          9          6          4          4  
 14:       33 *       14         11          7          5          4  
 15:       35.*       18         12          9          5          5  
 16:       43 *       19         14         10          7          5  
 17:       46 *       23         15         12          8          6  
 18:       54 *       24         17         13         10          6  
 19:       57.*       29         18         15         11          8  
 20:       67 *       31         20         16         13          9  
 21:       70.*       36         21         18         14         11  
 22:       81 *       38         25         19         16         12  
 23:       85 *       43         26         21         17         14  
 24:       96 *       45         30         22         19         15  
 25:      100.*       50         31         24         20         17  
 26:      113 *       52         35         25         22         18  
 27:      117.*       59         36         27         23         20  
 28:      131 *       61         41         28         25         21  
 29:      136 *       68         43         32         26         23  
 30:      150 *       70         48         33         28         24  
 31:      155.*       78         50         37         29         26  
 32:      171 *       81         55         38         31         27  
 33:      176.*       89         57         42         32         29  
 34:      193 *       92         62         43         34         30  
 35:      199 *      100         64         47         35         32  
 36:      216 *      103         69         48         39         33  
 37:      222.*      111         71         53         40         35  
 38:      241 *      114         76         55         44         36  
 39:      247.*      124         78         60         45         38  
 40:      267 *      127         85         62         49         39  
 41:      274 *      137         87         67         50         41  
 42:      294 *      140         94         69         54         42  
 43:      301.*      151         96         74         55         46  
 44:      323 *      155        103         76         59         47  
 45:      330.*      166        105         81         60         51  
 46:      353 *      170        113         83         65         52  
 47:      361 *      181        116         88         67         56  
 48:      384 *      185        124         90         72         57  
 49:      392.*      196        127         95         74         61  
 50:      417 *      200        135         97         79         62  
 51:      425.*      213        138        102         81         66  
 52:      451 *      217        146        104         86         67  
 53:      460 *      230        149        111         88         71  
 54:      486 *      234        157        113         93         72  
\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  3:        1 *        1 *        1 *        1 *        1 *
  4:        4 *        1 *        1 *        1 *        1 *
  5:       10 *        3 *        1 *        1 *        1 *
  6:       20 *        6          2 *        1 *        1 *
  7:       35 *       12          5          2 *        1 *
  8:       56 *       20          8          4          2 *
  9:       84 *       30         12          7          3 *
 10:      120 *       45         20         10          6  
 11:      165 *       63         29         16          9  
 12:      220 *       84         40         22         12  
 13:      286 *      112         55         30         16  
 14:      364 *      144         70         40         22  
 15:      455 *      181         91         50         30  
 16:      560 *      227        112         65         39  
 17:      680 *      276        139         80         49  
 18:      816 *      335        168         98         60  
 19:      969 *      398        204        119         75  
 20:     1140 *      473        240        140         90  
 21:     1330 *      554        285        168        105  
 22:     1540 *      646        330        196        126  
 23:     1771 *      746        385        228        147  
 24:     2024 *      860        440        264        168  
 25:     2300 *      980        506        301        195  
 26:     2600 *     1114        572        346        223  
 27:     2925 *     1258        650        392        252  
 28:     3276 *     1411        728        441        288  
 29:     3654 *     1585        819        496        324  
 30:     4060 *     1773        910        555        360  
 31:     4495 *     1963       1015        618        405  
 32:     4960 *     2176       1120        684        450  
 33:     5456 *     2410       1240        759        495  
 34:     5984 *     2654       1360        837        550  
 35:     6545 *     2866       1496        918        605  
 36:     7140 *     3148       1632       1009        660  
 37:     7770 *     3454       1785       1101        726  
 38:     8436 *     3778       1938       1201        792  
 39:     9139 *     4120       2109       1306        858  
 40:     9880 *     4481       2280       1420        936  
 41:    10660 *     4861       2470       1540       1014  
 42:    11480 *     5261       2660       1660       1092  
 43:    12341 *     5681       2870       1794       1183  
 44:    13244 *     6112       3080       1930       1274  
 45:    14190 *     6574       3311       2074       1365  
 46:    15180 *     7058       3542       2227       1470  
 47:    16215 *     7564       3795       2380       1575  
 48:    17296 *     8093       4048       2551       1680  
 49:    18424 *     8645       4324       2725       1800  
 50:    19600 *     9221       4600       2913       1920  
 51:    20825 *     9821       4900       3103       2040  
 52:    22100 *                5200       3293       2176  
 53:    23426 *                5525       3503       2312  
 54:    24804 *                5850       3716       2448  
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=4,t,m,l=1) <= b :
Date  : Fri Dec 13 05:27:37 1996
Author: U.Mutlu
Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 4 
l <= 1295           l  = 1 
v <= 255            v <= 54 
b <= 1679615        b <= 9999
Trivial cases are: t=m=k (ie. Complete Design), t=m=1, v=k, (b=1)
"+" means bonus nbr
Key to the signs at the end of the entry b:
 [.] Non-trivial Steiner System with L=1 (exact covering, packing, t-design)
 [*] Sch馬heim Lower Bound (SLB) or a known higher Exact Lower Bound (ELB)
met
\t/m        2/2        2/3        2/4        2/5        2/6        2/7
v\        1+/1+      1+/2+      1+/3+      1+/4+      1+/5+      1+/6+
----------------------------------------------------------------------
  4:        1 *        1 *        1 *        1 *        1 *        1 *
  5:        3 *        1 *        1 *        1 *        1 *        1 *
  6:        3 *        2 *        1 *        1 *        1 *        1 *
  7:        5 *        2 *        2 *        1 *        1 *        1 *
  8:        6 *        2 *        2 *        2 *        1 *        1 *
  9:        8 *        4          2 *        2 *        2 *        1 *
 10:        9 *        4          3          2 *        2 *        2 *
 11:       11 *        6          3 *        3          2 *        2 *
 12:       12 *        6          3 *        3          3          2 *
 13:       13.*        8          5          3          3          3  
 14:       18 *        9          5          4          3          3  
 15:       19 *       11          7          4          4          3  
 16:       20.*       12          7          4          4          4  
 17:       26 *       14          9          6          4          4  
 18:       27 *       15          9          6          5          4  
 19:       31 *       16         11          8          5          5  
 20:       35 *       18         12          8          5          5  
 21:       37 *       19         14         10          7          5  
 22:       39 *       21         15         10          7          6  
 23:       46 *       22         17         12          9          6  
 24:       48 *       24         18         12          9          6  
 25:       50.*       25         19         14         11          8  
 26:       59 *       26         21         15         11          8  
 27:       61 *       31         22         17         13         10  
 28:       63.*       32         24         18         13         10  
 29:       73 *       33         25         20         15         12  
 30:       75 *       38         27         21         15         12  
 31:       78 *       39         28         22         17         14  
 32:       88 *       40         29         24         18         14  
 33:       91 *       46         31         25         20         16  
 34:       94 *       47         32         27         21         16  
 35:      105 *       51         34         28         23         18  
 36:      108 *       54         35         30         24         18  
 37:      111.*       57         37         31         25         20  
 38:      124 *       59         38         32         27         21  
 39:      127 *       64         39         34         28         23  
 40:      130.*       66         44         35         30         24  
 41:      144 *       70         45         37         31         26  
 42:      147 *       74         46         38         33         27  
 43:      151 *       76         51         40         34         28  
 44:      165 *       78         52         41         35         30  
 45:      169 *       85         53         42         37         31  
 46:      173 *       87         58         44         38         33  
 47:      188 *       89         59         45         40         34  
 48:      192 *       96         60         47         41         36  
 49:      196.*       98         66         48         43         37  
 50:      213 *      100         67         50         44         38  
 51:      217 *      109         71         51         45         40  
 52:      221.*      111         74         52         47         41  
 53:      239 *      113         77         57         48         43  
 54:      243 *      122         79         58         50         44  
\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  4:        1 *        1 *        1 *        1 *        1 *
  5:        4 *        1 *        1 *        1 *        1 *
  6:        6 *        3          1 *        1 *        1 *
  7:       12 *        4          2 *        1 *        1 *
  8:       14.*        6          2 *        2 *        1 *
  9:       25 *        9          5          2 *        2 *
 10:       30.*       14          7          4          2 *
 11:       47 *       19         10          5          3  
 12:       57 *       26         12          7          3 *
 13:       78 *       34         13         10          6  
 14:       91.*       43         20         12          8  
 15:      124 *       54         26         15         10  
 16:      140.*       66         28         20         12  
 17:      183 *       83         39         23         14  
 18:      207 *       99         44         28         17  
 19:      261        118         55         33         19  
 20:      285.*      133         60         40         25  
 21:      352 *      147         77         48         27  
 22:      385.*      179         87         56         34  
 23:      466 *      196        104         64         40  
 24:      510 *      237        114         73         42  
 25:      600 *      255        135         84         53  
 26:      650.*      298        148         96         58  
 27:      763 *      324        169        111         69  
 28:      819.*      380        182        123         74  
 29:      950 *      411        215        140         85  
 30:     1020 *      472        231        156         90  
 31:     1170        512        264        174        107  
 32:     1240.*      580        280        190        117  
 33:     1411 *      627        323        204        134  
 34:     1496.*      701        347        224        144  
 35:     1689 *      742        390        238        161  
 36:     1791 *      826        414        270        171  
 37:     1998 *      871        468        287        192  
 38:     2109.*      962        492        319        205  
 39:     2350 *     1014        546        336        226  
 40:     2470.*     1130        570        377        239  
 41:     2737 *     1252        637        395        260  
 42:     2877 *     1380        670        438        273  
 43:     3171       1443        737        462        306  
 44:     3311.*     1508        770        505        322  
 45:     3634 *     1575        851        531        355  
 46:     3795.*     1729        895        583        371  
 47:     4148 *     1815        976        609        404  
 48:     4332 *     1971       1020        665        420  
 49:     4716       2154       1110        696        463  
 50:     4900.*     2254       1160        757        487  
 51:     5317 *     2360       1250        796        530  
 52:     5525.*     2539       1300        857        554  
 53:     5976 *     2725       1413        897        597  
 54:     6210 *     2829       1469        965        621  
\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  4:        1 *        1 *        1 *        1 *
  5:        5 *        1 *        1 *        1 *
  6:       15 *        3 *        1 *        1 *
  7:       35 *        7 *        3 *        1 *
  8:       70 *       14 *        6          2 *
  9:      126 *       30         12          5  
 10:      210 *       50         20         10  
 11:      330 *       84         34         17  
 12:      495 *      126         56         28  
 13:      715 *      193         90         47  
 14:     1001 *      289        142         70  
 15:     1365 *      414        212        105  
 16:     1820 *      563        303        140  
 17:     2380 *      761        415        196  
 18:     3060 *     1015        554        252  
 19:     3876 *     1333        722        336  
 20:     4845 *     1723        926        420  
 21:     5985 *     2194       1166        540  
 22:     7315 *     2748       1451        660  
 23:     8855 *     3394       1781        825  
 24:    10626 *     4140       2166        990  
 25:    12650 *     5000       2606       1210  
 26:    14950 *     5977       3112       1430  
 27:    17550 *     7078       3684       1716  
 28:    20475 *     8319       4334       2002  
 29:    23751 *     9713       5062       2366  
 30:    27405 *                5881       2730  
 31:    31465 *                6791       3185  
 32:    35960 *                7806       3640  
 33:    40920 *                8926       4200  
 34:    46376 *                           4760  
 35:    52360 *                           5440  
 36:    58905 *                           6120  
 37:    66045 *                           6936  
 38:    73815 *                           7752  
 39:    82251 *                           8721  
 40:    91390 *                           9690  
 41:   101270 *                                 
 42:   111930 *                                 
 43:   123410 *                                 
 44:   135751 *                                 
 45:   148995 *                                 
 46:   163185 *                                 
 47:   178365 *                                 
 48:   194580 *                                 
 49:   211876 *                                 
 50:   230300 *                                 
 51:   249900 *                                 
 52:   270725 *                                 
 53:   292825 *                                 
 54:   316251 *                                 
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

On Fri, 13 Dec 1996 17:31:53 GMT, bm373592@muenchen.org (Uenal Mutlu) wrote:
>KEYWORDS: Covering Designs, t-Designs, Steiner Systems, Wheels,
>          Combinatorial Optimization, Set Covering Problem (SCP),
>          Constant Weight Codes, ...
>
>Today, I've posted my latest lists of COVERING DESIGNS to the
>newsgroup sci.math.num-analysis under the already existing subject
>"ANN: Some New Results in the Field of Discrete Math/Designs/Codes"
>
>I'll no longer crosspost to other groups as has been in the past;
>so from now on look mainly in sci.math.num-analysis for new results.
The lists are after this posting. IMHO, better do reply to 
this or the following mails, because only these contain only 
the mentioned sci.math.num-analysis in the follow-up field....
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=5,t,m,l=1) <= b :
Date  : Fri Dec 13 05:27:37 1996
Author: U.Mutlu
Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 5 
l <= 1295           l  = 1 
v <= 255            v <= 54 
b <= 1679615        b <= 9999
Trivial cases are: t=m=k (ie. Complete Design), t=m=1, v=k, (b=1)
"+" means bonus nbr
Key to the signs at the end of the entry b:
 [.] Non-trivial Steiner System with L=1 (exact covering, packing, t-design)
 [*] Sch馬heim Lower Bound (SLB) or a known higher Exact Lower Bound (ELB)
met
\t/m        2/2        2/3        2/4        2/5        2/6        2/7
v\        1+/1+      1+/2+      1+/3+      1+/4+      1+/5+      1+/6+
----------------------------------------------------------------------
  5:        1 *        1 *        1 *        1 *        1 *        1 *
  6:        3 *        1 *        1 *        1 *        1 *        1 *
  7:        3 *        2 *        1 *        1 *        1 *        1 *
  8:        4 *        2 *        2 *        1 *        1 *        1 *
  9:        5 *        2 *        2 *        2 *        1 *        1 *
 10:        6 *        2 *        2 *        2 *        2 *        1 *
 11:        7 *        4          2 *        2 *        2 *        2 *
 12:        9 *        4          3          2 *        2 *        2 *
 13:       10 *        5          3          3          2 *        2 *
 14:       12 *        6          3 *        3          3          2 *
 15:       13 *        7          3 *        3          3          3  
 16:       15 *        8          5          3          3          3  
 17:       16 *        9          5          4          3          3  
 18:       18 *       10          6          4          4          3  
 19:       19 *       11          7          4          4          4  
 20:       21 *       12          8          4          4          4  
 21:       21.*       13          9          6          4          4  
 22:       27 *       14         10          6          5          4  
 23:       28 *       16         11          7          5          5  
 24:       30 *       17         12          8          5          5  
 25:       30.*       18         13          9          5          5  
 26:       37 *       20         14         10          7          5  
 27:       38 *       21         15         11          7          6  
 28:       42         23         16         12          8          6  
 29:       44         25         17         13          9          6  
 30:       48 *       26         18         14         10          6  
 31:       50 *       27         19         15         11          8  
 32:       53         28         20         16         12          8  
 33:       54 *       30         21         17         13          9  
 34:       62 *       31         23         18         14         10  
 35:       63 *       33         24         19         15         11  
 36:       67         34         25         20         16         12  
 37:       68 *       36         27         21         17         13  
 38:       76 *       37         28         22         18         14  
 39:       78 *       39         30         23         19         15  
 40:       82         40         31         24         20         16  
 41:       82.*       42         33         25         21         17  
 42:       93 *       42         34         26         22         18  
 43:       96         48         35         27         23         19  
 44:       99         49         37         28         24         20  
 45:       99.*       51         38         30         25         21  
 46:      111 *       51         39         31         26         22  
 47:      114         57         41         32         27         23  
 48:      122         58         42         34         28         24  
 49:      130         60         44         35         29         25  
 50:      130 *       60         46         36         30         26  
 51:      140         67         47         38         31         27  
 52:      140         68         48         39         32         28  
 53:      140 *       72         49         41         33         29  
 54:      152 *       74         51         42         34         30  
\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  5:        1 *        1 *        1 *        1 *        1 *
  6:        4 *        1 *        1 *        1 *        1 *
  7:        5 *        3          1 *        1 *        1 *
  8:        8 *        3          2 *        1 *        1 *
  9:       12 *        5          2 *        2 *        1 *
 10:       17 *        7          2 *        2 *        2 *
 11:       20 *        9          5          2 *        2 *
 12:       29         12          6          4          2 *
 13:       34         16          8          4          3  
 14:       43         20         10          6          3  
 15:       57         25         13          8          3 *
 16:       67         33         14         10          6  
 17:       68.*       40         18         12          7  
 18:       94 *       49         23         14          9  
 19:      113         59         28         17         11  
 20:      138         72         32         20         13  
 21:      151         84         37         24         15  
 22:      184         95         40         28         18  
 23:      190        103         49         32         19  
 24:      234        116         54         36         22  
 25:      259        137         63         40         26  
 26:      260.*      156         68         45         30  
 27:      319 *      176         77         53         34  
 28:      372        197         86         59         38  
 29:      433        215         97         67         43  
 30:      483        231        102         74         48  
 31:      540        258        111         83         52  
 32:      601        280        125         92         57  
 33:      672        314        135        101         60  
 34:      740        348        136        108         69  
 35:      802        389        162        117         74  
 36:      878        435        181        127         83  
 37:      955        452        206        140         88  
 38:     1035        479        219        152         97  
 39:     1121        516        245        163        102  
 40:     1211        557        258        171        111  
 41:     1294        596        284        184        120  
 42:     1402        656        302        205        129  
 43:     1507        701        328        224        136  
 44:     1609        771        341        244        145  
 45:     1716        815        373        265        154  
 46:     1837        859        380        283        165  
 47:     1957        900        411        299        170  
 48:     2091        960        444        325        179  
 49:     2222       1054        450        344        193  
 50:     2358       1144        494        366        203  
 51:     2569       1244        519        382        204  
 52:     2775       1342        520        405        230  
 53:     2974       1453        579        421        249  
 54:     3213       1559        632        448        274  
\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  5:        1 *        1 *        1 *        1 *
  6:        5 *        1 *        1 *        1 *
  7:        9 *        3          1 *        1 *
  8:       20 *        5          3          1 *
  9:       30 *        9          4          2 *
 10:       51         14          7          2 *
 11:       66.*       22         10          5  
 12:      113 *       35         17          8  
 13:      157         50         27         14  
 14:      232         74         39         18  
 15:      300         99         54         28  
 16:      419        136         68         39  
 17:      492        193         68         50  
 18:      671        262        107         60  
 19:      850        341        144         81  
 20:     1096        415        199         96  
 21:     1251        492        252        117  
 22:     1573        624        329        132  
 23:     1771.*      789        407        179  
 24:     2237 *      971        511        223  
 25:     2706       1099        616        270  
 26:     3306       1269        751        314  
 27:     3906       1482        886        389  
 28:     4669       1768       1054        457  
 29:     5427       2083       1224        532  
 30:     6232       2436       1439        600  
 31:     6780       2711       1650        719  
 32:     7785       3010       1913        792  
 33:     8930       3333       2152        911  
 34:                3883       2475        984  
 35:         .      4469       2799       1163  
 36:                5091       3175       1342  
 37:                5555       3545       1521  
 38:                6043       4010       1700  
 39:                6555       4472       1922  
 40:                7520       5018       2101  
 41:         .      8565       5514       2347  
 42:                9684       6151       2502  
 43:                           6783       2824  
 44:                           7519       3022  
 45:         .                 8232       3344  
 46:                           9076       3542  
 47:    35673.*                9937       4008  
 48:    39821 *                           4474  
 49:                                      4943  
 50:                                      5412  
 51:         .                            6012  
 52:                                      6612  
 53:         .                            7212  
 54:                                      7812  
\t/m        5/5        5/6        5/7
v\        4+/4+      4+/5+      4+/6+
-------------------------------------
  5:        1 *        1 *        1 *
  6:        6 *        1 *        1 *
  7:       21 *        4 *        1 *
  8:       56 *       11          3 *
  9:      126 *       25          8  
 10:      252 *       51         17  
 11:      462 *      100         32  
 12:      792 *      177         59  
 13:     1287 *      303        110  
 14:     2002 *      496        200  
 15:     3003 *      784        342  
 16:     4368 *     1196        554  
 17:     6188 *     1759        857  
 18:     8568 *     2520       1272  
 19:    11628 *     3535       1826  
 20:    15504 *     4868       2548  
 21:    20349 *     6591       3474  
 22:    26334 *     8785       4640  
 23:    33649 *                6091  
 24:    42504 *                7872  
 25:    53130 *                      
 26:    65780 *                      
 27:    80730 *                      
 28:    98280 *                      
 29:   118755 *                      
 30:   142506 *                      
 31:   169911 *                      
 32:   201376 *                      
 33:   237336 *                      
 34:   278256 *                      
 35:   324632 *                      
 36:   376992 *                      
 37:   435897 *                      
 38:   501942 *                      
 39:   575757 *                      
 40:   658008 *                      
 41:   749398 *                      
 42:   850668 *                      
 43:   962598 *                      
 44:  1086008 *                      
 45:  1221759 *                      
 46:  1370754 *                      
 47:  1533939 *                      
 48:  1712304 *                      
 49:  1906884 *                      
 50:  2118760 *                      
 51:  2349060 *                      
 52:  2598960 *                      
 53:  2869685 *                      
 54:  3162510 *                      
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=6,t,m,l=1) <= b :
Date  : Fri Dec 13 05:27:37 1996
Author: U.Mutlu
Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 6 
l <= 1295           l  = 1 
v <= 255            v <= 54 
b <= 1679615        b <= 9999
Trivial cases are: t=m=k (ie. Complete Design), t=m=1, v=k, (b=1)
"+" means bonus nbr
Key to the signs at the end of the entry b:
 [.] Non-trivial Steiner System with L=1 (exact covering, packing, t-design)
 [*] Sch馬heim Lower Bound (SLB) or a known higher Exact Lower Bound (ELB)
met
\t/m        2/2        2/3        2/4        2/5        2/6        2/7
v\        1+/1+      1+/2+      1+/3+      1+/4+      1+/5+      1+/6+
----------------------------------------------------------------------
  6:        1 *        1 *        1 *        1 *        1 *        1 *
  7:        3 *        1 *        1 *        1 *        1 *        1 *
  8:        3 *        2 *        1 *        1 *        1 *        1 *
  9:        3 *        2 *        2 *        1 *        1 *        1 *
 10:        4 *        2 *        2 *        2 *        1 *        1 *
 11:        6 *        2 *        2 *        2 *        2 *        1 *
 12:        6 *        2 *        2 *        2 *        2 *        2 *
 13:        7 *        4          2 *        2 *        2 *        2 *
 14:        7 *        4          3          2 *        2 *        2 *
 15:       10          4          3          3          2 *        2 *
 16:       10          5          3 *        3          3          2 *
 17:       12 *        6          3 *        3          3          3  
 18:       12 *        6          3 *        3          3          3  
 19:       15          7          5          3          3          3  
 20:       16          8          5          4          3          3  
 21:       17          9          5          4          4          3  
 22:       19 *       10          6          4          4          4  
 23:       21 *       10          7          4          4          4  
 24:       22 *       11          7          4          4          4  
 25:       23 *       13          8          6          4          4  
 26:       24         13          9          6          5          4  
 27:       27 *       14          9          6          5          5  
 28:       28 *       14         10          7          5          5  
 29:       30         17         11          8          5          5  
 30:       31         17         12          8          5          5  
 31:       31.*       19         13          9          7          5  
 32:       38 *       19         13         10          7          6  
 33:       39 *       22         14         10          7          6  
 34:       42 *       22         15         11          8          6  
 35:       47         24         16         12          9          6  
 36:       50         24         17         12          9          6  
 37:       53         27         17         13         10          8  
 38:       57         28         18         14         11          8  
 39:       59         29         20         15         11          8  
 40:       59         31         20         16         12          9  
 41:       61         33         21         16         13         10  
 42:       63 *       34         21         17         13         10  
 43:       67         35         24         18         14         11  
 44:       71         36         24         19         15         12  
 45:       77         38         26         20         15         12  
 46:       81         40         26         20         16         13  
 47:       86         41         29         21         17         14  
 48:       93         43         29         22         18         14  
 49:       97         43         31         23         19         15  
 50:      100         46         31         24         19         16  
 51:      110         47         34         24         20         16  
 52:      113         48         34         25         21         17  
 53:      117         50         36         27         22         18  
 54:      117         52         36         27         23         18  
\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  6:        1 *        1 *        1 *        1 *        1 *
  7:        4 *        1 *        1 *        1 *        1 *
  8:        4 *        3          1 *        1 *        1 *
  9:        7          3          2 *        1 *        1 *
 10:       10 *        4          2 *        2 *        1 *
 11:       11 *        5          2 *        2 *        2 *
 12:       15          6          2 *        2 *        2 *
 13:       21          9          5          2 *        2 *
 14:       25         11          5          4          2 *
 15:       31         15          8          4          3  
 16:       38         16          8          5          3  
 17:       44         21         11          6          3 *
 18:       48         26         12          7          3 *
 19:       66         32         15          9          6  
 20:       74         39         18         10          6  
 21:       77         48         21         13          9  
 22:       77.*       54         22         15          9  
 23:      104 *       64         26         17         11  
 24:      116         70         30         20         12  
 25:      130         77         36         22         15  
 26:      130.*       88         40         26         16  
 27:      167 *       91         46         27         19  
 28:      189        106         50         31         22  
 29:      226        121         56         36         23  
 30:      237        132         62         41         26  
 31:      285        154         69         46         29  
 32:      312        165         73         51         32  
 33:      363        185         79         57         33  
 34:      400        199         86         63         37  
 35:      454        212         92         69         41  
 36:      494        239         96         74         45  
 37:      546        263        108         80         51  
 38:      591        288        115         87         55  
 39:      642        308        121         96         61  
 40:      686        326        125        102         65  
 41:      743        353        143        109         71  
 42:      800        372        151        116         75  
 43:      855        406        154        125         81  
 44:      915        424        154        131         87  
 45:      977        445        181        139         93  
 46:     1045        451        193        147         98  
 47:     1111        475        207        154        104  
 48:     1182        480        207        165        110  
 49:     1259        537        234        168        117  
 50:     1338        574        246        183        121  
 51:     1455        634        260        198        127  
 52:     1551        674        260        209        134  
 53:     1672        742        297        221        140  
 54:     1772        785        319        236        144  
\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  6:        1 *        1 *        1 *        1 *
  7:        5 *        1 *        1 *        1 *
  8:        7 *        3          1 *        1 *
  9:       12 *        3 *        3          1 *
 10:       20 *        7          3          2 *
 11:       32         10          5          2 *
 12:       41         14          6          2 *
 13:       66         21         10          5  
 14:       80         32         14          8  
 15:      118         43         21         12  
 16:      160         55         29         14  
 17:      209         74         37         19  
 18:      252         81         42         24  
 19:      343        129         54         32  
 20:      400        149         72         40  
 21:      522        178        103         52  
 22:      580        189        120         61  
 23:      751        260        134         73  
 24:      784        326        164         82  
 25:     1018        419        206        107  
 26:     1170        556        268        121  
 27:     1170.*      630        303        146  
 28:     1489 *      772        356        160  
 29:     1803        858        442        198  
 30:     2236       1025        503        236  
 31:     2678       1155        603        278  
 32:     3217       1357        668        320  
 33:     3784       1446        793        369  
 34:     4318       1644        866        412  
 35:     4863       1843       1001        461  
 36:     5453       2030       1080        504  
 37:     6095       2143       1260        595  
 38:     6796       2556       1396        652  
 39:     7550       2681       1615        743  
 40:     8375       2926       1744        800  
 41:     9241       3337       2002        922  
 42:         .      3526       2116        980  
 43:                4103       2418       1102  
 44:                4438       2579       1160  
 45:                5059       2838       1306  
 46:                5587       3074       1364  
 47:                6219       3399       1535  
 48:                6827       3593       1568  
 49:                7705       3993       1750  
 50:                8406       4294       1921  
 51:         .      9346       4609       1954  
 52:                           5018       2188  
 53:                           5408       2340  
 54:                           5821       2340  
\t/m        5/5        5/6        5/7
v\        4+/4+      4+/5+      4+/6+
-------------------------------------
  6:        1 *        1 *        1 *
  7:        6 *        1 *        1 *
  8:       12 *        4          1 *
  9:       30 *        7          3  
 10:       50         14          4  
 11:      100         22          9  
 12:      132.*       38         14  
 13:      245 *       62         28  
 14:      377        105         45  
 15:      609        173         75  
 16:      808        253        129  
 17:     1227        381        191  
 18:     1548        544        245  
 19:     2210        765        352  
 20:     2900       1026        489  
 21:     3996       1379        688  
 22:     4692       1863        933  
 23:     6197       2428       1262  
 24:     7084.*     3086       1660  
 25:     9321 *     3917       2171  
 26:                4894       2778  
 27:                6141       3529  
 28:         .      7527       4402  
 29:                9278       5456  
 30:                           6668  
 31:                           8107  
 32:                           9737  
 33:                                 
 34:         .                       
 35:                                 
 36:         .                       
 37:                                 
 38:                                 
 39:                                 
 40:                                 
 41:                                 
 42:         .                       
 43:                                 
 44:                                 
 45:                                 
 46:         .                       
 47:                                 
 48:   285384.*                      
 49:   325205 *                      
 50:                                 
 51:                                 
 52:         .                       
 53:                                 
 54:         .                       
\t/m        6/6        6/7
v\        5+/5+      5+/6+
--------------------------
  6:        1 *        1 *
  7:        7 *        1 *
  8:       28 *        4 *
  9:       84 *       12 *
 10:      210 *       30 *
 11:      462 *       66 *
 12:      924 *      132 *
 13:     1716 *      264  
 14:     3003 *      511  
 15:     5005 *      951  
 16:     8008 *     1680  
 17:    12376 *     2648  
 18:    18564 *     4101  
 19:    27132 *     6315  
 20:    38760 *     9544  
 21:    54264 *    14293  
 22:    74613 *           
 23:   100947 *           
 24:   134596 *           
 25:   177100 *           
 26:   230230 *           
 27:   296010 *           
 28:   376740 *           
 29:   475020 *           
 30:   593775 *           
 31:   736281 *           
 32:   906192 *           
 33:  1107568 *           
 34:  1344904 *           
 35:  1623160 *           
 36:  1947792 *           
 37:  2324784 *           
 38:  2760681 *           
 39:  3262623 *           
 40:  3838380 *           
 41:  4496388 *           
 42:  5245786 *           
 43:  6096454 *           
 44:  7059052 *           
 45:  8145060 *           
 46:  9366819 *           
 47: 10737573 *           
 48: 12271512 *           
 49: 13983816 *           
 50: 15890700 *           
 51: 18009460 *           
 52: 20358520 *           
 53: 22957480 *           
 54: 25827165 *           
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

REPORT ON NEW OR IMPROVED RESULTS OF COVERING DESIGNS C(v,k,t,m,l,=b):
Design param     : C(23,6,5,5,1,=6197)
Author/Pgm/Method: I got it from Rade Belic (100721.1571@CompuServe.COM)
Date of creation : <= 96/12/12
Old bound was    : 6200
Remarks          : 
Design param     : C(21,6,4,6,1,=103)
Author/Pgm/Method: I got it from F.L.Oats (CZPU02A@prodigy.com)
Date of creation : <= 96/12/12
Old bound was    : 104
Remarks          : 
Design param     : C(17,6,4,4,1,=209)
Author/Pgm/Method: I got it from F.L.Oats (CZPU02A@prodigy.com)
Date of creation : <= 96/12/12
Old bound was    : 210
Remarks          : 
Design param     : C(21,6,5,6,1,=1379)
Author/Pgm/Method: I got it from F.L.Oats (CZPU02A@prodigy.com)
Date of creation : <= 96/12/12
Old bound was    : 1401
Remarks          : 
Design param     : C(17,7,6,6,1,=2140)
Author/Pgm/Method: I got it from A.Muehl (adolf.muehl@univie.ac.at)
Date of creation : <= 96/12/11
Old bound was    : 
Remarks          : 
Design param     : C(34,5,3,4,1,=360)
Author/Pgm/Method: I got it from A.Muehl (adolf.muehl@univie.ac.at)
Date of creation : <= 96/12/11
Old bound was    : 
Remarks          : 
Design param     : C(35,5,3,4,1,=402)
Author/Pgm/Method: I got it from A.Muehl (adolf.muehl@univie.ac.at)
Date of creation : <= 96/12/11
Old bound was    : 
Remarks          : 
Design param     : C(38,5,3,4,1,=479)
Author/Pgm/Method: I got it from A.Muehl (adolf.muehl@univie.ac.at)
Date of creation : <= 96/12/11
Old bound was    : 
Remarks          : 
New simple constructions: thru combining etc. (see first mail for ref [1]):
  C(33,6,4,7,1,=369)  (old: 370)
  C(35,6,4,7,1,=461)  (old: 462)
  C(22,7,5,7,1,=346)  (old: 347)
  C(22,7,6,7,1,=4381) (old: 4436)
  C(23,7,6,7,1,=6244) (old: 6275)
  C(24,7,6,7,1,=8614) (old: 8669)
(the above results were the last ones I added to the posted lists;
ie. these results are already in the lists)
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=7,t,m,l=1) <= b :
Date  : Fri Dec 13 05:27:37 1996
Author: U.Mutlu
Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 7 
l <= 1295           l  = 1 
v <= 255            v <= 54 
b <= 1679615        b <= 9999
Trivial cases are: t=m=k (ie. Complete Design), t=m=1, v=k, (b=1)
"+" means bonus nbr
Key to the signs at the end of the entry b:
 [.] Non-trivial Steiner System with L=1 (exact covering, packing, t-design)
 [*] Sch馬heim Lower Bound (SLB) or a known higher Exact Lower Bound (ELB)
met
\t/m        2/2        2/3        2/4        2/5        2/6        2/7
v\        1+/1+      1+/2+      1+/3+      1+/4+      1+/5+      1+/6+
----------------------------------------------------------------------
  7:        1 *        1 *        1 *        1 *        1 *        1 *
  8:        3 *        1 *        1 *        1 *        1 *        1 *
  9:        3 *        2 *        1 *        1 *        1 *        1 *
 10:        3 *        2 *        2 *        1 *        1 *        1 *
 11:        4 *        2 *        2 *        2 *        1 *        1 *
 12:        5          2 *        2 *        2 *        2 *        1 *
 13:        6          2 *        2 *        2 *        2 *        2 *
 14:        6 *        2 *        2 *        2 *        2 *        2 *
 15:        7 *        4          2 *        2 *        2 *        2 *
 16:        8          4          3          2 *        2 *        2 *
 17:        9          4          3          3          2 *        2 *
 18:       10          5          3          3          3          2 *
 19:       11          6          3 *        3          3          3  
 20:       12 *        6          3 *        3          3          3  
 21:       13          7          3 *        3          3          3  
 22:       13 *        8          5          3          3          3  
 23:       16          9          5          4          3          3  
 24:       17          9          5          4          4          3  
 25:       18         10          6          4          4          4  
 26:       20         11          7          4          4          4  
 27:       20 *       12          7          4          4          4  
 28:       22         12          8          4          4          4  
 29:       24         13          9          6          4          4  
 30:       25         14          9          6          5          4  
 31:       26         15         10          6          5          5  
 32:       31         16         11          7          5          5  
 33:       33         17         12          8          5          5  
 34:       38         18         12          8          5          5  
 35:       40         19         13          9          5          5  
 36:       45         19         14         10          7          5  
 37:       47         20         15         10          7          6  
 38:       53         21         15         11          7          6  
 39:       55         22         16         12          8          6  
 40:       56         23         17         12          9          6  
 41:       56         24         18         13          9          6  
 42:       56         25         18         14         10          6  
 43:       56         26         19         15         11          8  
 44:       56         26         20         15         11          8  
 45:       56         29         21         16         12          8  
 46:       56         30         22         17         13          9  
 47:       56         31         23         18         13         10  
 48:       56         33         24         18         14         10  
 49:       56.*       33         25         19         15         11  
 50:       65 *       35         25         20         15         12  
 51:       66 *       37         26         21         16         12  
 52:       75         38         27         21         17         13  
 53:       77         39         28         22         18         14  
 54:       86         40         29         23         18         14  
\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  7:        1 *        1 *        1 *        1 *        1 *
  8:        4 *        1 *        1 *        1 *        1 *
  9:        4 *        3          1 *        1 *        1 *
 10:        6 *        3          2 *        1 *        1 *
 11:        8 *        3          2 *        2 *        1 *
 12:       11          4          2 *        2 *        2 *
 13:       13          6          2 *        2 *        2 *
 14:       15          8          2 *        2 *        2 *
 15:       15 *       11          5          2 *        2 *
 16:       25         14          5          4          2 *
 17:       28         17          7          4          3  
 18:       34         20          8          4          3  
 19:       44         26         10          5          3  
 20:       50         29         12          7          3 *
 21:       53         36         14          8          3 *
 22:       66         41         16         10          6  
 23:       74         49         19         12          6  
 24:       90         55         19         14          8  
 25:      102         63         21         16          9  
 26:      116         69         23         18         11  
 27:      130         80         26         19         12  
 28:      152         88         28         21         14  
 29:      155        100         30         23         16  
 30:      155        111         30         26         18  
 31:      155        124         40         29         20  
 32:      186        137         43         32         22  
 33:      205        151         49         35         23  
 34:      239        165         56         41         25  
 35:      259        181         62         44         27  
 36:      301        196         68         51         29  
 37:      322        214         78         56         31  
 38:      368        230         81         63         34  
 39:      390        249         87         69         34  
 40:      442        266         97         75         36  
 41:      468        288        103         82         38  
 42:      523        306        106         89         41  
 43:      550        330        119         94         43  
 44:      616        348        127        102         45  
 45:      646        378        140        108         45  
 46:      715        397        148        116         55  
 47:      745        429        164        122         58  
 48:      826        448        176        133         64  
 49:      859        486        189        141         71  
 50:      938        506        199        153         77  
 51:      989        546        205        162         83  
 52:     1066        566        208        174         90  
 53:     1129        613        221        185         96  
 54:     1206        634        229        198        102  
\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  7:        1 *        1 *        1 *        1 *
  8:        5 *        1 *        1 *        1 *
  9:        6 *        3          1 *        1 *
 10:       10 *        3          3          1 *
 11:       17          5          3          2 *
 12:       24          8          4          2 *
 13:       30         11          5          2 *
 14:       44         17          7          2 *
 15:       57         24         12          6  
 16:       86         37         17          7  
 17:      114         45         25         11  
 18:      152         60         29         12  
 19:      182         73         39         16  
 20:      225         91         49         20  
 21:      245        115         59         27  
 22:      253        141         75         34  
 23:      253.*      171         92         40  
 24:      357 *      209        110         47  
 25:      443        249        132         54  
 26:      573        281        152         60  
 27:      673        309        186         74  
 28:      833        354        213         87  
 29:      978        398        255        101  
 30:     1194        434        299        114  
 31:     1401        526        342        143  
 32:     1677        579        400        171  
 33:     1941        655        435        200  
 34:     2278        712        489        228  
 35:     2613        792        519        266  
 36:     3018        843        569        283  
 37:     3413       1035        605        297  
 38:     3896       1149        706        310  
 39:     4368       1308        757        339  
 40:     4931       1496        873        367  
 41:     5489       1721        935        405  
 42:     6142       1941       1073        435  
 43:     6782       2171       1181        478  
 44:     7544       2421       1298        498  
 45:     8289       2710       1342        506  
 46:     9153       3023       1452        506  
 47:                3369       1600        610  
 48:                3741       1774        696  
 49:                4107       1928        800  
 50:                4479       2103        886  
 51:                4923       2322       1016  
 52:                5359       2504       1116  
 53:                5856       2764       1246  
 54:                6404       2998       1346  
\t/m        5/5        5/6        5/7
v\        4+/4+      4+/5+      4+/6+
-------------------------------------
  7:        1 *        1 *        1 *
  8:        6 *        1 *        1 *
  9:        9 *        4          1 *
 10:       20 *        5          3  
 11:       34         10          3 *
 12:       59         17          6  
 13:       78         28         10  
 14:      143         47         20  
 15:      203         77         32  
 16:      321        112         51  
 17:      408        154         70  
 18:      616        220         95  
 19:      772        287        135  
 20:     1115        416        178  
 21:     1424        543        243  
 22:     1938        721        346  
 23:     2405        884        457  
 24:     3088       1144        571  
 25:     3769       1461        716  
 26:     4373       1880        895  
 27:     4680       2436       1163  
 28:     4680.*     2940       1422  
 29:     6169 *     3712       1754  
 30:     7912       4428       2188  
 31:                5453       2632  
 32:                6558       3235  
 33:                7915       3732  
 34:                9170       4525  
 35:                           5248  
 36:                           6249  
 37:                           7172  
 38:                           8432  
 39:                           9696  
 40:                                 
 41:                                 
 42:                                 
 43:         .                       
 44:                                 
 45:                                 
 46:                                 
 47:                                 
 48:                                 
 49:                                 
 50:                                 
 51:                                 
 52:         .                       
 53:                                 
 54:                                 
\t/m        6/6        6/7
v\        5+/5+      5+/6+
--------------------------
  7:        1 *        1 *
  8:        7 *        1 *
  9:       16 *        4  
 10:       45 *        8  
 11:       84         19  
 12:      177         35  
 13:      264         62  
 14:      509        100  
 15:      853        205  
 16:     1450        378  
 17:     2140        587  
 18:     3366        888  
 19:     4730       1335  
 20:     6935       2023  
 21:     9648       3049  
 22:                4381  
 23:         .      6244  
 24:                8614  
 25:         .            
 26:                      
 27:                      
 28:                      
 29:         .            
 30:                      
 31:                      
 32:                      
 33:                      
 34:                      
 35:         .            
 36:                      
 37:         .            
 38:                      
 39:                      
 40:                      
 41:                      
 42:                      
 43:         .            
 44:                      
 45:                      
 46:                      
 47:         .            
 48:                      
 49:         .            
 50:                      
 51:                      
 52:                      
 53:         .            
 54:                      
\t/m        7/7
v\        6+/6+
---------------
  7:        1 *
  8:        8 *
  9:       36 *
 10:      120 *
 11:      330 *
 12:      792 *
 13:     1716 *
 14:     3432 *
 15:     6435 *
 16:    11440 *
 17:    19448 *
 18:    31824 *
 19:    50388 *
 20:    77520 *
 21:   116280 *
 22:   170544 *
 23:   245157 *
 24:   346104 *
 25:   480700 *
 26:   657800 *
 27:   888030 *
 28:  1184040 *
 29:  1560780 *
 30:  2035800 *
 31:  2629575 *
 32:  3365856 *
 33:  4272048 *
 34:  5379616 *
 35:  6724520 *
 36:  8347680 *
 37: 10295472 *
 38: 12620256 *
 39: 15380937 *
 40: 18643560 *
 41: 22481940 *
 42: 26978328 *
 43: 32224114 *
 44: 38320568 *
 45: 45379620 *
 46: 53524680 *
 47: 62891499 *
 48: 73629072 *
 49: 85900584 *
 50: 99884400 *
 51:115775100 *
 52:133784560 *
 53:154143080 *
 54:177100560 *
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

KEYWORDS: Covering Designs, t-Designs, Steiner Systems, Wheels,
          Combinatorial Optimization, Set Covering Problem (SCP),
          Constant Weight Codes, ...
Today, I've posted my latest lists of COVERING DESIGNS to the
newsgroup sci.math.num-analysis under the already existing subject
"ANN: Some New Results in the Field of Discrete Math/Designs/Codes"
I'll no longer crosspost to other groups as has been in the past;
so from now on look mainly in sci.math.num-analysis for new results.
I will not post the lists again, but I will post all new results I
find, or get from others, under the same subject to the same one 
newsgroup, so all msgs on this get grouped and listed under the 
same one subject. (Email me if you want the latest lists).
Discussions and other related topics (for example construction methods,
programs etc.) can also be posted under the same subject. Let's keep
this topic together.
You are invited to report your new and verified results too.
For an example see my following postings in sci.math.num-analysis.
-- Uenal Mutlu (bm373592@muenchen.org)   
   Math Research, Designs/Codes, Data Compression Algorithms, C/C++
   Loc  : Istanbul/Turkey + Munich/Germany

I am writing a serial interface and i need the exact information about
representation of floating point numbers, ie bit patterns etc.
  What is the standard on Windows NT?
  What is the standard on IRIX?
Information about reference manuals with IEEE or corresponding standard
numbers or is also needed.
-- 
Daniel Zagar
Cresita Engineering AB
addr:   Box 22226               e-mail: dza@cresita.se
        S-250 24 Helsingborg    phone:  +46 - (0)42 25 32 31
        Sweden                  fax:    +46 - (0)42 25 32 99

Combustion Dynamics wrote:
> 
> Are you talking about eigenvalues and eigenvectors?  If so, I know of
> two methods; subspace iteration, and the Lanczos method.  
There are a whole bunch of methods for finding extreme eigenvalues and
eigenvectors for large sparse matrices though most of them belong to the
family of subspace projection methods. Which one is best suitable
depends on the structure of matrix: is it positive definite, diag
dominant, symmetric, general? For more information check:
Y.Saad, Numerical Methods for Large Eigenvalue problems
Mike.

In article <58olum$1r52@rs18.hrz.th-darmstadt.de>,
Peter Spellucci  wrote:
>In article <58mkb1$oqq@news.lth.se>, tobias@maths.lth.se (Tobias Ryden) writes:
>|> Hello,
>|> 
>|> Does anybody has a solution or reference to the following problem?
>|> 
>|> Let G be a symmetric and positive definite matrix, block partitioned
>|> as
>|> 
>|> 
>|>    [G_11 G_12 G_13 ... G_1n]
>|>    [G_21 G_22 ....     G_2n]
>|>    [...                    ]
>|>    [...                    ]
>|>    [G_n1 G_n2 ....     G_nn]
>|> 
>|> where all blocks are square and equally sized, and G_ii is positive
>|> semi-definite for each i (which might be obvious?)
>|> 
>|> The problem is to minimize
>|> 
>|>    Q(a) = (\sum_{i=1}^n a_i G_ii)^{-1}
>|> 
>|>            * (\sum_{i,j} a_i a_j G_ij)
>|> 
>|>            * (\sum_{i=1}^n a_i G_ii)^{-1}
>|> 
>|> over all vectors a={a_i}, i=1,...,n, satisfying a_1+...+a_n=1 and a_i>=0
>|> for each i. The minimization should be done in the sense of "definiteness",
>|> i.e. if a* is the optimal vector and a is any other vector, then Q(a)-Q(a*)
>|> is positive semi-definite.
This means that this is not a scalar optimization problem but rather the
optimization is done with respect to the Lowner partial order (i.e. the
positive semidefinite partial order).
>|> 
>|> The middle part of the expression can be viewed as a quadratic form in
>|> the matrix blocks, while the outer parts, that are inverted, are linear
>|> combinations of the diagonal blocks.
>|> 
>|> The questions are if a vector a* that is optimal in the sense above exists,
>|> and, if so, if there is an algorithm to compute it?
>|> 
>looks like a typical PSD-problem. for solution and software look at:
>
>   semidefinite programming and determinant maximization
>
>   (solves c^Tx-log(detG(x)) subject to the linear matrix inequality
>   constraints G(x)>0, F(x)>0, subsumes LP, QP, and other convex problems,
>   includes the author's SP and MAXDET programs for which sources are
>   available, binaries for major platforms, very convenient to use with Matlab)
>     -> http://WWW-ISL.Stanford.EDU/~boyd/SDPSOL.html
>     -> ftp://isl.stanford.edu/pub/boyd
>   Solves semidefinite programs utilizing a Mehrotra-type predictor-corrector
>   step, uses sparse matrix structure, only binaries for major platforms,
>   includes documentation
>     -> ftp://ftp.is.titech.ac.jp/pub/OpRes/software/SDPA/
>hope this helps. peter
I think that this is problem is NOT a standard semidefinite programming
problem. The objective here is optimized with respect to the positive
semidefinite partial order and is NOT scalar valued but rather matrix
valued.
There are many results dealing with these types of problems.
One can change the above problem into a semi-infinite scalar valued
problem, i.e. the original problem
   min  Q(a) s.t. a in F  (F is the feasible set)
is equivalent to the problem
  min alpha  s.t.  trace (P*Q(a)) <= alpha, for all P pos semidef matrices
                      and a in F
i.e. the above has an infinite number of constraints indexed by the
set of pos semidef matrices; but now it also has a
scalar valued objective function. 
This is not necessarily the best way to approach the problem (there are
algorithms for semi-infinite programming - even in matlab optim toolbox)
The problem can also be approached by using vector valued
differentiation (see e.g. papers by Zowe and papers by Borwein
http://www.cecm.sfu.ca/~jborwein/)
To date I have not seen any serious algorithmic papers on this problem.
If someone has a reference to one, I would be very interested.
-- 
||Henry Wolkowicz                |Fax:   (519) 725-5441
||University of Waterloo         |Tel:   (519) 888-4567, 1+ext. 5589
||Dept of Comb and Opt           |email:  henry@orion.math.uwaterloo.ca
||Waterloo, Ont. CANADA N2L 3G1  |URL: http://orion.math.uwaterloo.ca/~hwolkowi

The COG of any triangle is given by the intersection of the lines
bisecting the angles.
fred a.

Archive-name: num-analysis/faq/part1
Last-modified: 1996 December 14
q10. FAQ: Numerical Analysis & Associated Fields Resource Guide
Welcome!  My intent here is to provide reviews of software, texts,
and other resources instead of simply a listing.  My experience is
that for someone looking for a package or system, reviews by previous
users can be a lifesaver.
If you have any suggestions, comments, or contributions please send
them to me at:   sullivan@mathcom.com
Other reviews would be most welcome!  If you use a mathematical
package or set of programs and would care to write one to twenty
sentences on it, please let me know.  If you have a favorite text
or two you'd like to recommend, please let me know.
Sigh, and now the legalities ...
The information contained in this document is believed to be true,
but no guarantees of accuracy are made, and there is no liability
of any sort for any consequences of its use.
This document may be copied and/or reproduced providing that:
	* the use is for non-commercial purposes only, and
	* all copies contain this copyright notice:
	* Copyright 1995-6 S. J. Sullivan
See:
	* q20, "NA FAQ: Introduction"
	* q30, "NA FAQ: Overview of Recent Additions"
	* q40, "NA FAQ: Table of Contents"
	* q50, "NA FAQ: Acknowledgements"
Steve Sullivan
sullivan@mathcom.com
Mathcom, Inc.
8555 Hollyhock St., Lafayette, CO  80026  USA
=========================================================================
q20. NA FAQ: Introduction
Where to find this FAQ:
On the web:
http://www.indra.com/~sullivan/q10.html   Mathcom
This FAQ is usually available from MIT's rtfm and its mirrors:
ftp://rtfm.mit.edu/pub/usenet/news.answers/num-analysis/faq/part1  MIT's rtfm
If not, a compressed (with gzip) version is at:
ftp://ftp.mathcom.com/mathcom/nafaq.txt.gz  Mathcom ftp
A mirror site in Germany, courtesy of Jens Burmeister
(jb@numerik.uni-kiel.de), is:
http://www.numerik.uni-kiel.de/faqs/tda/q10.html  Mirror in Germany
Abbreviations used in this document:
NA	Numerical Analysis
###	Denotes "to be filled in later".  This is work in progress,
and probably always will be.
[]	Reviews are associated with the name of the reviewer in brackets.
Those reviews marked [SJS] are by myself.
[author]	indicates text taken from a package documentation.
10^12	10 to the power 12.  In Fortran, that's 10**12;
in C that's pow(10,12).
x(i)	the i'th element of vector x.  In C, that would be x[i].
Instead of the normal question/answer form, this FAQ is organized
as an outline ... hopefully, you'll find your questions answered here.
=========================================================================
q30. NA FAQ: Overview of Recent Additions
q125.11, "Matlab to C++ Compiler and C++ Matrix Class Library"
MAT, a Matlab Compatible C++ Matrix Class Library.
q260.2.7, "QMG"
[author]: QMG is free software for fully automatic unstructured finite
element mesh generation in two and three dimensions.  It can generate meshes
for complex polyhedral domains with nonmanifold features.
q265.1, "Optimization, Linear and Non-Linear Programming"
NEOS Guide to Optimization Software
q260.6, "Books and References for PDE and FEM"
Books by Wolfgang Hackbusch.
q520.1, "Comparative Reviews on Symbolic Algebra Packages"
Michael Wester's page on comparative reviews of symbolic
algebra packages.
q570, "Constraints"
University of New Hampshire Constraint Computation Center
As well as numerous other updates.
=========================================================================
q40. NA FAQ: Table of Contents
	* q10, "FAQ: Numerical Analysis & Associated Fields Resource Guide"
	* q20, "NA FAQ: Introduction"
	* q30, "NA FAQ: Overview of Recent Additions"
	* q40, "NA FAQ: Table of Contents"
	* q50, "NA FAQ: Acknowledgements"
	* 
	* q105, "What is Numerical Analysis?"
	* q110, "Indices of NA Software on the Net"
	* q112, "Indices of Commercial NA Software"
	* q115, "Libraries of NA Software on the Net"
	* q120, "NA Packages on the Net"
	* q125, "Commercial NA Libraries and Packages"
	* q135, "Newsgroups for NA"
	* q140, "Professional Societies for NA"
	* q145, "Electronic Newsletters for NA"
	* q150, "Electronic Journals for NA"
	* q155, "Online Preprints for NA"
	* q160, "Miscellaneous Web Sites for NA"
	* q165, "Books, With and Without Software, for NA"
Specialized Subfields Within Numerical Analysis
	* q205, "Dense (Non-Sparse) Linear Algebra Systems"
	* q207, "Sparse Linear Algebra Systems"
	* q210, "Random Number Generators (RNGs)"
	* q215, "Function Evaluation"
	* q220, "Finding Roots"
	* q230, "Curve Fitting, Data Modelling, Interpolation, Extrapolation"
	* q240, "Transforms (FFT, etc) and digital signal processing (DSP)"
	* q245, "Wavelets"
	* q250, "Integration and Ordinary Differential Equations (ODEs)"
	* q253, "Stochastic Differential Equations"
	* q255, "N-Body and Particle Simulation"
	* q260, "Partial Differential Equations (PDEs) and Finite Element Modeling (FEM)"
	* q265, "Operations Research: Minimization, Optimization"
	* q270, "Computational Geometry"
	* q285, "Graphics and Scientific Visualization"
	* q290, "Miscellaneous NA Software"
Associated Fields
	* q505, "Probability and Statistics"
	* q510, "Chaos Theory (Nonlinear Dynamics)"
	* q520, "Symbolic Algebra"
	* q530, "Cryptography (Cryptology)"
	* q540, "Fractals"
	* q550, "Neural Networks"
	* q560, "Discrete algorithms"
	* q570, "Constraints"
	* q580, "Genetic Algorithms"
	* q590, " Simulated Annealing"
Teaching and Academic Software
	* q800, "Teaching and Academic Software"
===========================================================================
q50. NA FAQ: Acknowledgements
Many thanks to all those who've given their time and advice
in creating this FAQ, including:
   Bob Berman			berman@FERMAT.macsyma.com
   Ronald F Boisvert		boisvert@cam.nist.gov
   Ted Brown			tbrown@tekotago.ac.nz
   John Chandler		jpc@a.cs.okstate.edu
   Luiz Henrique de Figueiredo	lhf@csgrs6k1.uwaterloo.ca
   Bill Frensley		frensley@utdallas.edu
   Pawel Gora			gora@if.uj.edu.pl
   Amara Graps			agraps@netcom.com
   Vijay Gupta			gupta@acsu.Buffalo.edu
   Doug Hart			hart@de01.denver.waii.com
   Albert Hines			ahines@howmet.com
   Charles Knechtel             doug@scn.org
   Zdislav V. Kovarik		kovarik@mcmail.cis.McMaster.CA
   Dave Linder			dwl@apmaths.uwo.ca
   George Marsaglia		geo@stat.fsu.edu
   Pierre Maxted		pflm@star.maps.susx.ac.uk
   Allen Mcintosh		mcintosh@bellcore.com
   Sean O riordain		sor@inrets.fr
   Daniel Pfenniger		pfennige@scsun.unige.ch
   Daniel Pick			pick@lune.math.tau.ac.il
   Brian Ripley			ripley@stats.ox.ac.uk
   Ramin Samadani		ramin@leland.Stanford.EDU
   Robert Schneiders		robert@Informatik.RWTH-Aachen.DE
   Peter Somlo			somlo@zeta.org.au
   Tim Strotman			tim.strotman@sdrc.com
   N. Sukumar			n-sukumar@nwu.edu
   Stephen Vavasis		vavasis@CS.Cornell.EDU
   Dave Watson			watson@maths.uwa.edu.au
Many thanks also to the organizers of the many services
listed herein - Netlib, the NIST guide, NA-Net, CAIN, the NASA
Graphics site, and numerous other indices and informative web pages.
===========================================================================
q105. What is Numerical Analysis?
NA is the union of theoretical and computational investigation into
the computer solution of mathematical problems.  NA generally includes
those problems involving continuous functions of real or complex
variables, as opposed to solely discrete variables and functions.
The mixing of theoretical and computational concerns leads to
a strong emphasis on algorithms:  what are the time and memory
usage properties of a certain algorithm?  What errors are introduced
by an algorithm?
The compuational aspects of NA usually take place within
the scope of floating-point arithmetic, and are implemented on
machines ranging from super-computers through PCs to hand-calculators.
The theoretical aspects extend into fields such as Calculus,
Differential Equations, and Analysis.  The field of Linear Algebra
is so often used to model physical systems that the theoretical
study of Linear Algebra is in itself often considered to be
NA at work.
Primary areas of theoretical concern in NA are:
	* global/local error bounding
	* stability of algorithms
	* rates of convergence of algorithms
Primary areas of computational concern in NA are:
	* roundoff error
	* global/local error and its tolerance
	* time and memory requirements of computation
	* High Performance Computing (HPC)
	* parallel computing
	* architechture/platform specific details.
===========================================================================
q110. Indices of NA Software on the Net
For indices of packages oriented towards symbolic algebra,
see q520, "Symbolic Algebra".
The NIST Guide to Available Mathematical Software (Formerly called GAMS)
http://gams.nist.gov/  NIST Guide to Mathematical Software
or telnet to: gams.nist.gov
[SJS]:
Maintained by National Institute of Standards and Technology (NIST)
An index and server for a wide variety of mathematical
software, including most of netlib (see q115.1, "Netlib").
Much of the software is in Fortran.  If you prefer to speak C++ or C,
see q160.1, "C++ Resources", and q115.2, "Fortran, C, and f2c".
[Ronald Boisvert]:
The main focus is on fine-grained software components, e.g.
subroutines, although information about some larger packages are
included.  As of November 1995, nearly 10,000 components from more
than 90 packages have been cross-indexed using a detailed
tree-structured problem classification system.  Both freely available
software (from netlib or developed at NIST) and commercial packages
(used by NIST) are indexed, although source code is available only for
non-commercial software.
===================================
q112. Indices of Commercial NA Software
A large list of commercial NA products may be found at:
http://www.cray.com/PUBLIC/APPS/DAS/  Cray
The Directory of commercial software, by International Computer
Programs, Inc., is at:
http://www.icp.com/softinfo/  ICP
Finally, for packages oriented towards symbolic algebra,
see q520, "Symbolic Algebra".
===========================================================================
q115. Libraries of NA Software on the Net
Libraries are collections of source code, and source code packages.
Much of the code is in Fortran.  If you prefer to speak C++ or C,
see q160.1, "C++ Resources", and q115.2, "Fortran, C, and f2c".
The main library by far is q115.1, "Netlib".
For statistical software, the best resource is q115.3, "Statlib".
Other libraries are q115.4, "NCAR's Mathematical and Statistical Libraries"
and q115.5, "Hensa Unix Parallel Archive".
	* q115.1, "Netlib"
	* q115.2, "Fortran, C, and the f2c Translator"
	* q115.3, "Statlib"
	* q115.4, "NCAR's Mathematical and Statistical Libraries"
	* q115.5, "Hensa Unix Parallel Archive"
	* q115.6, "Modula-3 NA Library"
	* q115.7, "Forth Numerical/Scientific Library"
	* q115.8, "Eiffel Numerical/Scientific Library"
	* q115.9, "Lisp Numerical/Scientific Libraries"
===========================================================================
q115.1. Netlib
NetLib is probably the world's largest repository of numerical
methods programs. It is located at Oak Ridge National Laboratory,
Knoxville, Tennessee, and at AT&T; Bell Laboratories, Murray Hill, NJ.
email: send message "help" to either:
   netlib@ornl.gov
   netlib@research.att.com
http://www.netlib.org                               Netlib main
http://www.netlib.org/netlib/netlib_faq.html        Netlib FAQ
http://www.netlib.org/master/expanded_liblist.html  Netlib index
ftp://netlib.att.com/netlib                         Netlib via ftp
Netlib mirrors:
http://www.netlib.no/  Netlib in Norway
or email to: netlib@nac.no
http://www.hensa.ac.uk/ftp/mirrors/netlib/master/  Netlib in England
or email to: netlib@ukc.ac.uk
http://elib.zib.de/netlib/master/readme.html  Netlib in Germany
or:
http://elib.zib-berlin.de/netlib  Netlib in Germany
or email to: anonymous@elib.zib-berlin.de
ftp://draci.cs.uow.edu.au/netlib/  Netlib in Australia
or email to: netlib@draci.cs.uow.edu.au
Netlib in Taiwan: email only: netlib@nchc.edu.tw
Some gems of netlib:
Machine/architecture dependant Basic Linear Algebra Subroutines
(BLAS) are the keystone of Netlib.
LAPACK, in Fortran 77, is the modern replacement
of EISPACK, LINPACK, etc.
CLAPACK is a C version of LAPACK.  See the Caution on
Using Arrays in q115.2, "Fortran, C, and f2c".
LAPACK++ is a C++ version of, sadly, only a subset of LAPACK.
LAPACK++ is work in progress, and hopefully the full
functionality of LAPACK will be supported soon.
ScaLAPACK is for distributed memory machines.
===================================
q115.2. Fortran, C, and the f2c Translator
For C++ and C resources, see q160.1, "C++ Resources".
Most of the programs in netlib are in Fortran.  However, netlib
contains an excellent Fortran-to-C conversion utility, f2c.
While f2c produces working C code, it is visually complex
and ugly.  Using f2c on a large package like LAPACK can require
a good deal of time to get all the options correct.
Fortunately, LAPACK has already be converted to C: see CLAPACK.
The utility f2c can also be invoked by email.  Send email
to netlib@research.att.com, with the subject "execute f2c",
and body containing the non-confidential Fortran program to be converted.
But the email option is of use only for very small, simple programs,
since a resulting C program of any size must be linked with the
f2c libraries.  Usually one will have to download the f2c package
anyway to generate the libraries.  Generally it's easier
to download the f2c package, build the libraries and the
f2c conversion program, and do the conversion locally.
CAUTION: Programs created by f2c conversion use parameter passing
conventions different from most C or C++ programs.  Their
callers must create the appropriate parameters before using them.
See the file f2c.ps in the f2c distribution.
A good description of this issue may also be found in
the "readme" file for clapack in netlib.
===================================
q115.3. Statlib
Statlib is a huge repository of statistics related software and info.
Probability, statistics, random variables, distribution functions.
http://lib.stat.cmu.edu/   Statlib at CMU
ftp://lib.stat.cmu.edu     Statlib via ftp
email: send message "send index" to statlib@lib.stat.cmu.edu
===================================
q115.4. NCAR's Mathematical and Statistical Libraries
NCAR's libraries contain some overlap with netlib.
http://http.ucar.edu/SOFTLIB/mathlib.html  NCAR
===================================
q115.5. Hensa Unix Parallel Archive
General info, software, articles, etc., on parallel computing.
http://www.hensa.ac.uk/parallel/environments/pcn/  Hensa
Note: this web server can be very slow!
===================================
q115.6. Modula-3 NA Library
http://www.eskimo.com/~hgeorge/  Modula-3 NA
and pick the link to m3na.
This is a libraried collection of numerical analysis routines written
in Modula-3.  Includes linear algebra, roots, ffts, and a bit
of statistics.
===================================
q115.7. Forth Numerical/Scientific Library
http://www.taygeta.com/fsl/sciforth.html  Skip Carter's Forth Library at Taygeta
===================================
q115.8. Eiffel Numerical/Scientific Library
http://www.eiffel.com/products/math.html  Commercial Eiffel library at I.S.E.
===================================
q115.9. Lisp Numerical/Scientific Libraries
http://euler.bd.psu.edu/lispstat/   statistical tools.
http://setosa.uwaterloo.ca/~ftp/Quail/features.html   U. Waterloo
http://eksl-www.cs.umass.edu/research/clip-clasp-overview.html  instrumentation and statistical analysis packages
ftp://ftp.cs.cmu.edu/user/ai/lang/lisp/code/math/0.html  CMU's library
===========================================================================
q120. NA Packages on the Net
Packages generally include an NA library and an interpretive
language for a front end.
Also see q520, "Symbolic Algebra", for free symbolic algebra packages.
	* q120.1, "Octave"
	* q120.2, "RLaB"
	* q120.3, "Scilab"
	* q120.4, "Tela"
	* q120.6, "Medal"
	* q120.7, "Euler"
	* q120.8, "Prophet"
	* q120.9, "Yorick"
	* q120.10, "PETSc"
===================================
q120.1. Octave
http://bevo.che.wisc.edu/octave.html  Octave
ftp://www.che.wisc.edu/pub/octave     Octave via ftp
[Dave Lindner]: Octave is considered the closest-to-Matlab
of the Matlab clones.
[author]:
Octave is a high-level language, primarily intended for
numerical computations. It provides a convenient command line
interface for solving linear and nonlinear problems
numerically.
Octave can do arithmetic for real and complex scalars and matrices,
solve sets of nonlinear algebraic equations, integrate functions over
finite and infinite intervals, and integrate systems of ordinary
differential and differential-algebraic equations.
The Octave distribution includes a 200+ page Texinfo manual.
Two and three dimensional plotting is fully supported using gnuplot.
The underlying numerical solvers are currently standard
Fortran ones like Lapack, Linpack, Odepack, the Blas,
etc., packaged in a library of C++ classes.
===================================
q120.2. RLaB
http://www.eskimo.com/~ians/rlab.html   RLaB
ftp://csi.jpl.nasa.gov/pub/matlab/RLaB  RLaB via ftp
ftp://evans.ee.adfa.oz.au/pub/RLaB      RLaB via ftp in Australia
[author]:
Rlab is an interactive, interpreted scientific programming
environment. Rlab is a very high level language intended to provide
fast prototyping and program development, as well as easy
data-visualization, and processing.
Rlab is not a clone of languages such as those used by tools like
Matlab or Matrix_X/Xmath. However, as Rlab focuses on creating a good
experimental environment (or laboratory) in which to do matrix math,
it can be called "MATLAB-like" since the programming language
possesses similar operators and concepts.
===================================
q120.3. Scilab
http://zenon.inria.fr/Logiciels/SCILAB-eng.html  Scilab
ftp://ftp.inria.fr/INRIA/Scilab                  Scilab via ftp
[Dave Lindner]: Scilab is another good Matlab clone.
[author]:
Scilab is a high-level language for numerical computations
in a user-friendly environment. It features:
Elaborate data structures (polynomial, rational and string
matrices, lists, multivariable linear systems,...).
Sophisticated interpreter and programming language with
Matlab-like syntax.
Hundreds of built-in math functions (new primitives can easily be
added).
Stunning graphics (2d, 3d, animation).
Open structure (easy interfacing with Fortran and C via online
dynamic link).
Many built-in libraries :
	* Linear Algebra (including sparse matrices, Kronecker
	form, ordered Schur,...).
	* Control (Classical, LQG, H-infinity, ...).
	* Signal processing.
	* Simulation (various ode's, dassl,...).
	* Optimization (differentiable and non-differentiable, LQ solver).
	* Metanet (network analysis and optimization).
Symbolic capabilities through Maple interface.
===================================
q120.4. Tela
http://www.geo.fmi.fi/prog/tela.html  Tela
ftp://ftp.funet.fi/pub/sci/math/tela  Tela via ftp
General NA package with graphics, linear algebra, FFT, etc.
Is this another Matlab clone?
[author]:
It is mainly targeted for prototyping large-scale
numerical simulations and doing pre- and postprocessing for them, and
it replaces a compiled language like C++ or Fortran in this respect.
The feature set is therefore biased to operations needed in partial
differential equation solvers.
===================================
q120.6. Medal
ftp://excel2.uwaterloo.ca/pub  Medal
Apparently there is also available is a commercial version of Medal:
Email : medal@excel2.uwaterloo.ca
[author]:
MEDAL is a novel expert system development environment which is integrated
within a control system design environment, and which supports a tight
coupling of symbolic and numeric processing.  MEDAL supports the development
of coupled systems in engineering and science.
MEDAL (Matrix and Expert system Development Aid Language) is an interactive
program.  The language syntax of MEDAL is similar to the popular MATLAB
(Matrix Laboratory) language.  MEDAL retains all of the main features of
MATLAB, including the MATLAB syntax and M-files.
In addition, MEDAL includes an integrated expert system shell for the
development of knowledge-based systems which can perform
sophisticated numeric calculations.   Hence, the additional
expert system predicates extends the MATLAB command language syntax.
Also, MEDAL supports a rich set of data structure for representing
objects in the programming environment.  Knowledge can be
represented using facts, rules and frames.
Main features of MEDAL :
------------------------
	* interactive computing environment ( command-drive )
	* language syntax and user-interface similar to MATLAB
	* all basic MATLAB-type of matrix functions are provided
	* flexible 2-D graphics
	* design of linear control systems
	* packed matrix representation, as well as regular matrices
	* automatic loading of M-files ( open philosophy )
	* build-in knowledge base development facilities (expert shell )
	* knowledge repesentation : rules, facts, objects ( frames )
	* simple knowledge base of the Systematic Design Approach is included
	* runs on Sun Sparc workstations (X-window), PC (DOS), DEC (Ultrix)
References:
(1) Pang, G.K.H.,``Knowledge-based Control System Design'', in
Recent Advances in Computer-Aided Control Systems Engineering,
Jamshidi, M and  Herget, C.J. (ed.), Elsevier Science Publishers, 1992.
(2) Pang, G.K.H., ``A Knowledge Environment for an Interactive Control
System Design Package'', Automatica, Vol. 28. No. 3, pp. 473-491, May 1992.
===================================
q120.7. Euler
ftp://am.ku-eichstaett.de/pub        Euler via ftp
[author]:
EULER started as a MatLab clone. It is now a program, which can handle 
real, complex and interval numbers and matrices, has a 2D/3D graphics, a 
builtin modern programming language (extension of MatLab's), an exact 
scalar product, and the Windows 95 version can call functions in an 
external DLL. The OS/2 and Windows versions interact nicely with the GUI, 
and have a notebook style interface.
The Unix version is free, the OS/2 version free for educational use, and 
the Windows version cheap shareware.
These features make EULER an ideal tool for the tasks such as
	* Inspecting and discussing functions of one real or complex
	variable.
	* Viewing surfaces in parameter representation.
	* Linear algebra and eigenvalue computation.
	* Testing numerical algorithms.
	* Solving differential equations numerically.
	* Computing polynomials.
===================================
q120.8. Prophet
http://www-prophet.bbn.com/   Prophet
ftp://www-prophet.bbn.com     Prophet via ftp
email: prophet-info@bbn.com
[author]:
Prophet is an NIH-sponsored Unix workstation software package for life
science computing.  Prophet includes tools for data management,
statistical analysis, curve fitting, data graphing, mathematical
modeling, and genetic sequence analysis.
One of PROPHET's greatest assets is its new graphical
user interface . Employing the latest advances in software
technology, PROPHET lets you store,
analyze and present Data Tables, Graphs, Statistical Analyses and
Mathematical Modeling, and Sequence Analyses with high-resolution
graphics and multiple windows. Anyone, from the computer-naive to the
computer-sophisticate, can learn to use it quickly and effectively.
PROPHET is a National Computing Resource for Life Science Research
sponsored by the National Center for Research Resources of the
National Institutes of Health.
Unfortunately, prophet is distributed in binary form only.
It is large: it takes something like 65 MB disk space.
===================================
q120.9. Yorick
   wuarchive.wustl.edu: /languages/yorick/yorick-1.2.tar.gz
   sunsite.unc.edu: /pub/languages/yorick/yorick-1.2.tar.gz
   sunsite.unc.edu: /pub/Linux/apps/math/matrix/yorick-1.2.tar.gz
   netlib.att.com: /netlib/env/yorick-1.2.tar.gz
   netlib2.cs.utk.edu: /env/yorick-1.2.tar.gz
[author]
Yorick is an interpreted language.  It has:
	* A C-like language, but without declarative statements.  Operations
	between arrays require no explicit loops, which accounts for
	Yorick's high speed.  Scientific computing and numerical analysis
	are the goals of most Yorick sessions.
	* An X window system interactive graphics package.
	* A library of functions written in the Yorick language.
Because Yorick can read either text or binary files, it can be used
"out of the box" as a pre- and post-processor for most existing
physics simulation programs.
As a pre-processor, you can write a Yorick program that produces
complicated input files for a simulation.  These might be based on
output from other programs, or might require evaluation of complicated
functions or involve a lot of repetition.
As a post-processor, Yorick allows you to compare the results of
several simulations or to analyze results of a single simulation in
ways you did not forsee when you ran it.
===================================
q120.10. PETSc
ftp://info.mcs.anl.gov/pub/petsc   PETSc by ftp
http://www.mcs.anl.gov/petsc/petsc.html  PETSc by www
[author]:
Portable, Extensible Toolkit for Scientific Computation (PETSc).
   PETSc provides many tools for the parallel (and uniprocessor),
numerical solution of PDEs that require solving large-scale, sparse
nonlinear systems of equations.  PETSc includes nonlinear and linear
equation solvers that employ a variety of Newton techniques and Krylov
subspace methods. In addition, PETSc provides several parallel sparse
matrix formats, including compressed row, block compressed row, and
block diagonal storage.
   PETSc is fully usable from Fortran, C and C++, and runs portably on
on most UNIX systems.  PETSc uses MPI for all parallel communication.
   One of the unique features of PETSc is that it enables the
application programmer to easily and efficiently assemble parallel
vectors and sparse matrices.  Users can create complete application
programs for the parallel solution of nonlinear PDEs without writing
much explicit message-passing code themselves.
   In addition, PETSc is designed to facilitate extensibility.  Thus,
users can incorporate customized solvers and data structures when
using the package.
===========================================================================
q125. Commercial NA Libraries and Packages
Commercial libraries and packages tend to merge, so I've combined
them in one category.  Typically a commercial product contains:
	* a library of numerical routines
	* graphics routines
	* an interactive interpreted language
Many symbolic algebra packages also contain NA packages.
For info on these packages, see q520, "Symbolic Algebra".
An good article on commercial software is:
Braham, Robert.  "Math & Visualization: new tools, new frontiers",
IEEE Spectrum 32, 11 (November 1995), p. 19-36.
The article contains tables comparing large number of commercial products.
There is no mention of the many excellent free products though.
	* q125.1, "NAG"
	* q125.2, "IMSL and PVWAVE"
	* q125.3, "Matlab and Simulink"
	* q125.4, "WavBox"
	* q125.5, "CraySoft Libraries"
	* q125.6, "IDL"
	* q125.7, "Comparison of IDL and Matlab"
	* q125.8, "Mlab"
	* q125.9, "Gauss"
	* q125.10, "MathViews"
	* q125.11, "Matcom: Matlab to C++ Compiler"
===================================
q125.1. NAG
http://www.nag.co.uk:70/  NAG in England
http://www.nag.com/       NAG in USA
[SJS]: Numerical, symbolic, statistical, and visualization libraries in
Fortran 77, Fortran 90, C, Pascal, Ada, and parallel machine versions.
High performance Fortran 90 and Fortran 77 compilers.
NAG Ltd (The Numerical Algorithms Group)
   Wilkinson House
   Jordan Hill Road
   OXFORD
   OX2 8DR
   UK
   Tel: +44 1865 511245
NAG Inc
   1400 Opus Place
   Suite 200
   Downers Grove
   IL 60515-5702
   USA
   Tel: +1 708 971 2337
===================================
q125.2. IMSL and PVWAVE
http://www.vni.com/indexall.html    Visual Numerics, Inc.
[SJS]: IMSL is a set of routines in C, C++, and Fortran
libraries for general NA, statistics and graphics.
PVWAVE is a visual programming environment built on top of IMSL.
Visual Numerics, Inc.
   IMSL and Stanford Graphics Products
   9990 Richmond Avenue, suite 400
   Houston, Texas 77042-4548
   USA
   Tel: 800-222-4675
   Tel: 713-784-3131
   FAX: 713-781-9260
   e-mail: marketing@houston.vni.com
Visual Numerics, Inc
   PV-WAVE Products Division
   6230 Lookout Road
   Boulder, Colorado 80301
   USA
   Tel: 800-447-7147
   Tel: 303-530-9000
   FAX: 303-530-9329
   info@boulder.vni.com
[author]:
	* Comprehensive Mathematical Functionality
		* integration and differentiation
		* transforms
		* differential equations
		* linear systems
		* interpolation and approximation
		* eigensystem analysis
		* optimization
		* special functions
		* basic matrix/vector operations
		* nonlinear equations
		* utilities
	* Extensive Statistical Functionality
		* basic statistics
		* tests of goodness-of-fit
		* time series analysis and forecasting
		* analysis of variance
		* regression
		* nonparametric statistics
		* correlation
		* random number generation
		* cluster analysis
		* categorical and discrete data analysis
		* probability distribution functions and inverses
		* factor analysis
		* utilities
	* Exponent Graphics includes:
		* Presentation quality graphs for application development
		* Application program interface provides easy access to either
		FORTRAN or C
		* Two function calls can automatically produce one of over 30
		different plot types.
		* Maximum flexibility for modifying plot chacteristics
		* Powerful interactive editing and customization tools
		* CGM, PostScript, HPGL and other device drivers
		* Support for popular graphics accelerators and output systems
		* Full Windows-based online documentation with hypertext links
PV-WAVE is a software environment for solving problems requiring the
application of graphics, mathematics, numerics and statistics to data
and equations.
PV-WAVE uses an intuitive fourth generation language (4GL) that
analyzes and displays data as you enter commands. With it you can
perform complex analysis, visualization, and application
development quickly and interactively.
Robust integrated graphics, numerics, data I/O, and data management
has made PV-WAVE the number one selling Visual Data Analysis software
family.
PV-WAVE and the IMSL numerical and statistical routines, which are
seamlessly integrated in PV-WAVE Advantage, are being used by more
than 300,000 technical professionals on workstations worldwide.
===================================
q125.3. Matlab and Simulink
http://www.mathworks.com/    Mathworks
The MathWorks, Inc.
   24 Prime Park Way
   Natick, MA 01760-1500
   (508) 653-1415
For a comparison of Matlab and IDL, see
q125.7, "Comparison of IDL and Matlab".
[SJS]: Matlab is an interactive general NA package, including graphics.
A huge variety of "toolboxes" are available, both from the
vendor and on the net, for various specialized NA areas:
control systems, neural nets, optimization, symbolic math,
and on and on.
Simulink is modeling, simulation, and system analysis tool.
[author]:
MATLAB is a technical computing environment for high-performance
numeric computation and visualization. MATLAB integrates numerical
analysis, matrix computation, signal processing, and graphics in an
easy-to-use environment where problems and solutions are expressed
just as they are written mathematically - without traditional
programming.
MATLAB has evolved over a period of years with input from many users.
In university environments, it has become the standard instructional
tool for introductory courses in applied linear algebra, as well as
advanced courses in other areas. In industrial settings, MATLAB is
used for research and to solve practical engineering and mathematical
problems. Typical uses include general purpose numeric computation,
algorithm prototyping, and special purpose problem solving with matrix
formulations that arise in disciplines such as automatic control
theory, statistics, and digital signal processing (time-series
analysis).
MATLAB also features a family of application-specific solutions that
we call toolboxes. Very important to most users of MATLAB, toolboxes
are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment in order to solve particular classes of
problems. Areas in which toolboxes are available include signal
processing, control systems design, dynamic systems simulation,
systems identification, neural networks, and others.
SIMULINK is a tool for modeling, analyzing, and simulating an
extraordinarily wide variety of physical and mathematical systems,
including those with nonlinear elements and those which make use of
continuous and discrete time.
As an extension of MATLAB, SIMULINK adds many features specific to
dynamic systems while retaining all of MATLAB's general purpose
functionality.
Using SIMULINK, you model a system graphically, sidestepping much of
the nuisance associated with conventional programming.
===================================
q125.4. WavBox
http://www.wavbox.com/  Wavbox
email: info@wavbox.com
A wavelet Toolbox for Matlab.
[author]:
A software toolbox for wavelet transforms and adaptive
wavelet packet decompositions with new satisficing search algorithms.
Requires Matlab.
===================================
q125.5. CraySoft Libraries
http://www.cray.com/PUBLIC/product-info/craysoft/CS_home_txt.html  Cray product info
http://www.cray.com/           Cray main
http://www.cray.com/craysoft/  Craysoft main
email: crayinfo@cray.com
Corporate Headquarters:
   Cray Research, Inc.
   655 Lone Oak Drive
   Eagan, Minnesota 55121
   (800) 289-2729 or (612) 683-3030,
[author]
Fortran 90 compilers and NA library for Cray, Sparc,
Macintosh, and Windows environments.
	* Seismic migration
	* Structural analysis
	* Financial modeling
	* Decision support analysis
	* General scientific
	* Computational chemistry
	* Computational physics
	* Intelligence, signal and image processing
	* Electronic simulation
===================================
q125.6. IDL
Research Systems Inc.
http://www.rsinc.com/  Research Systems, Inc.
Research Systems, Inc.
   2995 Wilderness Place
   Boulder, CO  80301  USA
   Phone: 303-786-9900
   email: info@rsinc.com
For a comparison of IDL and Matlab, see
q125.7, "Comparison of IDL and Matlab".
IDL binaries are available at:
ftp://ftp.rsinc.com/pub/idl               Research Systems, Inc.
ftp://boulder.colorado.edu/pub/idl        U. of Colorado
ftp://ftp.Germany.EU.net/shop/CreaSo/IDL  Germany
Following are two sets of comments on IDL:
1. By Pierre Maxted
2. By Amara Graps
================
1. Comments by Pierre Maxted
I find that IDL is good for "playing" with data. This works well for
astronomers who seem to end up always wanting to do something a little
different to last time to data that always has slightly different quirks
everytime. I also find that it is a rather easy language in which to
write my own routines. This is probably because I can start with
interactive IDL to get the feel for what the data is like and what I want
to do with it - this then becomes a simple batch file which can be turned
into a routine if the procedure is useful - this seems to be a natural
way to develop things. These libraries of routines are what makes IDL
really powerful in my opinion. I found that adding the astronomy user's
library to IDL was like adding wheels to a car. I would recommend to
anyone considering using IDL to find out what libraries are out
there (e.g. starting at the IDL WWW homme page).
Whatever you add to the FAQ, make one point clear - calling IDL a fancy
plotting package is like calling a Formula 1 racing car good for picking
up the kids from school - IDL can do plotting, but that is not its
strength.
Well, I agree that the hard copy manuals are rather opaque but Version 4
of IDL has online help (Hyperhelp) that is rather good - especially since
it had text searching capabilites so that you can go straight to the bit
you need (usually).
================
2. Comments by Amara Graps
Following is an excerpt of comments by [Amara Graps]:
For the full text of her review, please see:
http://www.amara.com/papers/miscpap.html   Amara Graps' Papers
ftp://ftp.amara.com/papers/IDL_Matlab.txt  Amara Graps' Papers via ftp
If you install IDL without a valid license, you will get IDL's
7 minute demo mode. This mode is designed for users who are
considering buying the package.
IDL is a vector-based language that makes it easy to manipulate arrays
and matrices.  I've done testing comparing IDL speed to
Fortran in various actions, and IDL was as fast as a Fortran program for
the IDL array computations where loops were removed (i.e., when
using implicit loops in IDL instead of explicit FOR statments).
The scientific functions and procedures that come with IDL are often all
that scientists need.  In addition, there are net archives
containing contributed routines.  The archives at
John Hopkins and at Goddard are especially good (see below).
The language, for the most part is "open", i.e. you can see the
text of any particular procedure or function, in case you doubt the
technique, or want to modify it. Some functions and procedures are
black-box, intrinsic functions or procedures, but not nearly as many as
Matlab (see below) are.
Most work in IDL is done at the command line level.  However, IDL supplies
rudimentary "widgets" to wrap a GUI around your procedures and
functions. You can create buttons, menus, scrollboxes etc.
Three-d plotting is currently not very well documented, and the way that
IDL does it is very convoluted. Other users and I have complained about
it, and I think RSI are taking steps to better document how to do it.
Image procesing and animation is pretty slick.
If you need to do "slicing and dicing" of a volume, in a way like
Spyglass Dicer, IDL has a really great widget routine to do it.
The IDL plots are high quality enough to use in initial journal
submissions.
RSI's support (writing to support@rsinc.com) is pretty good, I
usually get responses within 24-34 hours. You have to pay yearly technical
support costs, though- about $200 year (don't remember exactly how much).
The Usenet group: comp.lang.idl-pvwave has some smart programmers giving
answers if you don't want to pay for the IDL technical support. RSI
usually doesn't answer questions on that newsgroup (they have a company
policy against promoting IDL there because it's shared by two products:
IDL and PVWave).
I've never liked the IDL documention very much. The information that you
need probably *is* in the manuals, but it's somewhat hard to find (the
manuals are organized in a wierd way).  [Note, however, the comments
by Pierre Maxted above].
The anonymous ftp sites below contain public domain IDL code.
http://fermi.jhuapl.edu/www/s1r/idl/idl.html  JHU/APL/S1R IDL library
ftp://fermi.jhuapl.edu/pub/idl                JHU/APL/S1R IDL library via ftp
NASA IDL Astronomy User's Library, run by Wayne Landsman:
http://idlastro.gsfc.nasa.gov/homepage.html   NASA IDL Astro Library
ftp://idlastro.gsfc.nasa.gov/pub              NASA IDL Astro Library via ftp
ftp://iuesn1.gsfc.nasa.gov     IUE RDAF library at NASA
ftp://cetus.colorado.edu/pub   IUE RDAF library at U. of Colorado
ftp://ftp.astro.psu.edu/pub/nefftp/icur  ICUR Spectral Analysis Software
ftp://legacy.gsfc.nasa.gov/rosat/software/idl  IDL ROSAT software
ftp://ftp.sma.ch/pub/idlmeteo  IDLmeteo library
ftp://eos.crseo.ucsb.edu/pub/idl  ESRG library
Hal Mueller has a Digital U.S. Map browser based on images
created by Ray Sterner at Johns Hopkins University using IDL:
http://www.zilker.net/~hal/apl-us//  Map browser
E. Loren Buhle, Jr. Ph.D. made a page on AVS IN MEDICAL TREATMENT
PLANNING which also discusses IDL:
http://archive.xrt.upenn.edu/0h/buhle/manuscripts/avs94_paper.html  Medical Treatment Planning
===================================
q125.7. Comparison of IDL and Matlab
Following is an excerpt of a paper by [Amara Graps]:
For the full text of her review, please see:
http://www.amara.com/papers/miscpap.html   Amara Graps' Paper
ftp://ftp.amara.com/papers/IDL_Matlab.txt  Amara Graps' Paper via ftp
IDL is a package that began life as an image-processing utility that has
grown to be a general-purpose numerical analysis tool. Matlab started as
a numerical analysis package that now includes [at extra cost] image
processing tools. Now the two have a similar scientific data-analysis
environment, with capabililties to build GUI programs and do very robust
data analysis.
(Note: all prices are approximate October 1995 prices - SJS)
They each cost about the same: ~$1500 for Mac and PC versions and more for
Unix (~4000 -- single user to $15,000 -- unlimited number of users).
Matlab is popular among education institutions because it has exceptional
educational discounts. If you are an academic, Matlab can be had for
$495 and each toolbox only $195. My NASA colleagues thought that
MathWorks "nickled- and-dimed" them with the costs of the Toolkits (like
the signal processing toolkit), but given what you get, it probably
isn't that unreasonable.
IDL seems to be more widespread in the NASA communities probably because
the original developer used several spacecraft teams (Pioneer Venus and
Voyager) as test beds for the IDL software.
IDL is more of a true programming language. Matlab has scripts and
functions and no way to explicitly type a variable. IDL has programs,
procedures, and functions and a language syntax sort of like a cross
between Fortran, Pascal, and APL. If you have programmed in Fortran
before, then the syntax will be a snap to learn. Matlab's syntax is much
more compact than IDL's. For example: x = transpose(y) in IDL is x=y' in
Matlab.
Matlab has many more built-in, intrinsic functions than IDL.
MatLab has many optional Toolkits, such as a Signal Processing
Toolkit and an Image Processing Toolkit, which are libraries
of more intrinsic functions.
Reading and writing files, and handling formats such as GIF,
PICT, GDF, and custom formats, seems much easier in IDL than MATLAB.
Handling directories is difficult in MATLAB when run on non-unix
machines.
Matlab has more types of graph types than IDL, and handling
colors is simpler than IDL. However, I found most
other Matlab graphical programming non-intuitive. It uses a system where
each element in a graph is an "object." These objects can have
sub-objects. So to change an element in a graph, say the axis color, you
have to first find the object (a "get" function), and then set it to the
color you want. IDL has system variables storing all graphics elements
which can be easily changed. One can also customize a graph upon making
the graph, with a keyword.
IDL's technical support is pretty good, but Matlab's is better. Post
a question on comp.soft-sys.matlab and either a developer, the company
president, or a tech support person will respond that day. You can call
them, too, but it's not a toll-free call.
===================================
q125.8. Mlab
http://www.civilized.com/MLAB.htmld/  Civilized Software
Civilized Software, Inc.
   7735 Old Georgetown Rd. #410
   Bethesda, MD 20815
   U.S.A.
   1-301-656-4714
   1-301-656-1069 fax
   Email: csi@civilized.com
[author]:
MLAB, (for Modeling LABoratory), is a program for interactive
mathematical and statistical modeling. MLAB was originally developed
at the National Institutes of Health. It includes curve-fitting,
differential equations, statistics and graphics as some of its major
capabilities.
===================================
q125.9. Gauss
email: info@aptech.com
Aptech Systems has a web page on Gauss at:
http://www.netaxis.qc.ca/~j.breslaw  Aptech Systems
Aptech Systems, Inc., Tel: (206) 432-7855, Fax: (206) 432-7832
   23804 South East Kent-Kangley Road
   Maple Valley, WA 98038 USA
   (206) 432-7855
[author]:
The GAUSS Mathematical and Statistical System is available for IBM PCs and
compatibles as well as UNIX workstations
As a complete programming language, the GAUSS system is both
flexible and powerful. Immediately available to the GAUSS user is a wide
variety of statistical, mathematical and matrix handling routines. Powerful
data handling capabilities including a data loop allow transformations in a
data set by directly using variable names inexpressions. This greatly
simplifies data transformations and makes for shorter more readable programs.
GAUSS can be used in either command mode(interactively) or in edit mode. In
command mode; one-line commands, or small screen-resident programs, can be
issued and the results of calculations seen immediately. In edit mode you
can write complex programs and store them in files.
GAUSS has over 400 functions built in, including LINPACK and EISPACK
routines.
===================================
q125.10. MathViews
http://www.mathwizards.com  MathViews
[author] MathViews for Windows is matlab look-alike. It
has a full set of linear algebra and signal processing
functionality.  It provides easy access to: matrix and linear
algebra, digital signal processing, instrument control, image
processing, time series analysis, data visualization and 
waveform display and editing.
MathViews is highly compatible with the matlab syntax and will
execute most matlab m-files with no changes.
We also have WaveTool.
WaveTool is an interactive software tool for creating, editing
and analyzing captured waveshapes. Waveforms can be created
using any combination of drawing, math expressions (matlab
syntax), insertion from a library of waveforms or data values
pasted from other applications such as Microsoft Excel.
===================================
q125.11. Matlab to C++ Compiler and C++ Matrix Class Library
http://www.mathtools.com  Mathtools
or email: info@mathtools.com
[author]:
MATCOM V2 is a Matlab(R) to C++ compiler. MATCOM creates MEX files 
and standalone C++ applications, with royalty free distribution.
MATCOM translates Matlab code to C++, which is compiled by your
optimizing C++ compiler. The resulting code runs significantly faster
than the original interpreted source.
Prior knowledge of C++ is not necessary to use MATCOM. The compilation
is fully automated by a smart project manager.
Fully functional, time limited evaluation version of MATCOM V2 can be
downloaded freely from the MathTools web site.
MAT, a Matlab Compatible C++ Matrix Class Library,
is designed for development of advanced 
scientific high-level C++ code. Evalution version of the MAT 
can be downloaded from the home page noted above.
The library includes Complex math, Binary and unary operators, 
Powerful indexing capabilites, Signal processing, File I/O, Linear
algebra, String operations and Graphics. Over 300 mathematical 
functions are included in MAT.
MAT supports matrices of doubles, floats, ints and chars
mixed in the program. Images can be stored in matrices of chars,
using 1/8 memory storage. On many applications, where 8 digits of
precision are sufficient, float-precision matrices can save half
the memory usage. Memory allocation and  de-allocation is managed
automatically.
===========================================================================
q135. Newsgroups for NA
Newsgroups related to numerical analysis are:
sci.math.num-analysis	The primary group for NA issues.
sci.math.symbolic	Covers symbolic algebra: Mathematica, Maple,
Macsyma, Derive, Reduce, Mcad, etc.
comp.soft-sys.math.mathematica:  Devoted to Mathematica.
sci.op-research		Covers operations research, linear programming,
non-linear programming.
sci.stat.math		Covers probability and statistics.
sci.math		Covers a broad range of mathematical subjects, at
levels from trivial to advanced.
sci.math.research	Covers advanced mathematics, and
is generally theoretical as opposed to applied.
===========================================================================
q140. Professional Societies for NA
	* q140.1, "The (AMS) American Mathematical Society"
	* q140.2, "(SIAM) The Society for Industrial and Applied Mathematics"
	* q140.3, "ACM, Inc. (Association for Computing Machinery)"
	* q140.4, "IEEE  The Institute of Electrical and Electronic Engineers"
===================================
q140.1. The (AMS) American Mathematical Society
http://www.ams.org/  AMS
email: ams@math.ams.org
General organization information, preprint titles, pointers to
other preprint servers and net resources.  Also includes:
MathDoc, the document delivery service offered by the AMS, provides
copies of original journal, collection and conference proceedings
articles from publications covered by Mathematical Reviews, Current
Mathematical Publications, and the MathSci database.  This costs
roughly US$14. per ten pages, as of October 1995.
MathSciNet is a searchable database available on the World Wide Web.
It is based on the data in Mathematical Reviews and Current
Mathematical Publications, leading publications that catalog and
review research literature in mathematics.  This costs roughly
US$5500. per year, as of October 1995.
===================================
q140.2. (SIAM) The Society for Industrial and Applied Mathematics
http://www.siam.org/  SIAM
email: siam@siam.org
General organizational information, tables of contents
of SIAM journals, and recently accepted articles.
Society for Industrial and Applied Mathematics
3600 University City Science Center
Philadelphia, PA 19104-2688
(215) 382-9800
Journals include:
SIAM Scientific Computing
SIAM Matrix Analysis
SIAM Control and Optimization
===================================
q140.3. ACM, Inc. (Association for Computing Machinery)
http://acm.org/  ACM
email: ACMHELP@acm.org
General organizational information, info on journals and conferences.
Of particular interest are:
Transactions on Mathematical Software (TOMS)
http://www.acm.org/pubs/toms/  ACM TOMS
Collected Algorithms of the ACM (CALGO)
Software can be found in netlib (toms directory); see q115.1, "Netlib".
SIGNUM (Special Interest Group in Numerical Mathematics)
http://www.acm.org/sig_hp/SIGNUM.html  ACM SIGNUM
ACM Headquarters
One Astor Plaza
1515 Broadway
New York, New York 10036
212-869-7440
===================================
q140.4. IEEE  The Institute of Electrical and Electronic Engineers
http://www.ieee.org  IEEE
email: member.services@ieee.org
General organizational information, journals, books, conferences.
   Tel: (800) 678-IEEE
   Tel: (212) 705-7900
===========================================================================
q145. Electronic Newsletters for NA
http://www.netlib.org/na-net/na_home.html  NA-Net
http://www.netlib.org/na-digest/topics     NA-Net Index
email: nanet@na-net.stanford.edu
[author]:
The NA-Net is a system developed to serve the community of numerical
analysts and other researchers. The Na-Net provides two independent
databases and a weekly digest to its members. The Email Database is
the electronic mail address of each of its members, and is capable
of forwarding mail to them. In addition, this database serves as the
distribution list for the NA Digest (see below). The White Pages
Database is basically a directory service. It provides a way to
exchange personal information among its members. Contained in the
database are phone numbers, postal mailing addresses, research
interests, affiliations, etc. The NA Digest is a way to provide its
members with a weekly collection of articles on topics related
to numerical analysis and those who practice it. To get on the
mailing list for the digest and enter yourself in their database,
you can use email or the World Wide Web. Take advantage of this very
useful service!
===========================================================================
q150. Electronic Journals for NA
Indices of Journals
See the large list of online journals, and other resources,
at Penn State's Mathematics web site.
http://www.math.psu.edu/OtherMath.html  Penn State Mathematics
See also:
http://rattler.cameron.edu/swjpam/  The Southwest Journal of Pure and Applied Mathematics
===================================
BIT
http://math.liu.se/BIT/  BIT
BIT emphasizes numerical methods in approximation, linear algebra, and
ordinary and partial differential equations, but also publishes papers
in areas such as numerical functional analysis and numerical
optimization.
===================================
ETNA (Electronic Transactions in Numerical Analysis).
http://etna.mcs.kent.edu/  ETNA
An online peer reviewed journal.  Keyword searching.
Most documents are postscript and may be downloaded.
Started in 1993.  Indexes only itself.
===================================
EJDE, The Electronic Journal of Differential Equations
http://ejde.math.swt.edu/  EJDE
A purely on-line peer-reviewed journal.
===================================
The Electronic Journal of Linear Algebra
http://gauss.technion.ac.il/iic/ela/  Electronic J. of Linear Algebra
===================================
New York Journal of Mathematics
http://nyjm.albany.edu:8000/nyjm.html  NY J. of Mathematics
Appears more abstract than applied.  Started in 1994.  Indexes only itself.
===========================================================================
q155. Online Preprints for NA
General
See the listings for professional societies, especially the AMS,
in q140, "Professional Societies for NA".
Springer-Verlag
Preprints: See the Springer-Verlag preprint service via email.
Not free.
http://www.springer.de/server/services.html  Springer Verlag
Virtual Library Math Journals Preprints
http://euclid.math.fsu.edu/Science/Preprints.html  Virtual Lib Math Jnls Preprints
Links to numerous organizations offering preprints.
===========================================================================
q160. Miscellaneous Web Sites for NA
See also:
	* q160.1, "C++ Resources for NA"
	* q160.2, "Math FAQ"
Caltech guide to mathematics resources
http://www.ama.caltech.edu/resources.html  Caltech Guide to Math Resources
Good collection of pointers to quality sites.
Penn State's Math Guide
http://www.math.psu.edu/OtherMath.html  Penn State Math Guide
Huge site with information on many fields within mathematics.
U. C. Berkeley
gopher://math.berkeley.edu     U.C. Berkeley gopher site (large)
ftp://math.berkeley.edu /pub   U.C. Berkeley ftp site (large)
http://math.berkeley.edu/      U.C. Berkeley ftp site (small)
Berkeley has a large gopher & ftp site, including courseware, pointers
to inet libraries, lecture notes, seminars, and software.
Indiana University:  Mathematical Computing Resources Guide
http://www.indiana.edu/~statmath/mathsites.html   Indiana University.
An excellent large site.
The World-Wide Web Virtual Library: Mathematics
http://euclid.math.fsu.edu/Science/math.html  Virtual Lib: Mathematics
Specialized fields (topology, cryptography, optimization, etc),
academic departments, miscellaneous math societies and institutes,
pointers to commercial software, newsgroups, nice collection
of preprints pointers, electronic journals
U. Tennessee Knoxville Mathematics Archives WWW Server
http://archives.math.utk.edu/  U. Tenn Knoxville Math Archives
MathSoft's Favorite Mathematical Constants
http://www.mathsoft.com/asolve/constant/constant.html  Mathsoft Constants
Constants and algorithms for their generation.
Tomasz Plewa's list of www sites for numerical methods
http://tonic.physics.sunysb.edu/docs/num_meth.html  Plewa's NA page, USA
http://www.math.psu.edu/dna/num_methods.html  Plewa's NA page, USA
http://zar.unizar.es/www/num_meth.html  Plewa's NA page, Spain
http://www.labyrinth.net.au/~ctrans/tomasz.html  Plewa's NA page, Australia
Amara Graps' list of science links
http://www.amara.com/science/science.html  Amara Graps' list
A Catalog of Mathematics Resources on WWW and the Internet
http://mthwww.uwc.edu/wwwmahes/files/math01.html  Catalog of Math Resources
By M. Maheswaran, University of Wisconsin Marathon Center.
Another large site, with a sizeable section on Applied Mathematics.
Altug Koker's list of simulation software
http://piranha.eng.buffalo.edu/simulation/comp.simulation/FAQ.html   Simulation Software
(See his Q15.).  Contains pointers to software for:
aerospace, automotive, chemistry / biotechnology, graphics and imaging,
electronics / electrical engineering, petroleum
The Yahoo server's index of Mathematics topics.
http://www.yahoo.com/Science/Mathematics  Yahoo's Math index
Includes commercial products, conferences, journals, and various
subfields of mathematics, primarily in applied mathematics.
Scientific Applications on Linux Web Page
http://lusk1.mines.edu/hjjou/linux_old.html  Scientific Apps on Linux
Contents:
	* Commercial Scientific Software
	* MatLab Alike and Related Packages
	* Mathematics and Statistics
	* Finite or Boundary Element
	* Numerical Analysis
	* Signal, Communication, Data and Image Processing/Visualization
	* CAD, Graph, Drawing and Modelling Tools
	* Scientific Data Plotting Packages
	* Scientific Data Plotting Libraries
	* General Purpose Graphic Libraries
	* Word Processing, Typesetting And Office Software
	* X-Window GUI Construction
	* Misc Scientific Packages or Libraries and Links
	* Other Links
For a wide variety of links to mathematical and scientific software, see:
http://www-ocean.tamu.edu/~baum/linuxlist-m.html  S. Baum's site
===================================
q160.1. C++ Resources for NA
Ajay Shah's index of resources for NA in C or C++
http://www.math.psu.edu/FAQ/numcomp-free-c.txt  Ajay Shah's C++ Resources
ftp://usc.edu/pub/C-numanal/numcomp-free-c.gz  Ajay Shah's C++ Resources via ftp
ftp://ftp.math.psu.edu/pub/FAQ/numcomp-free-c  Ajay Shah's C++ Resources via ftp
The Object-Oriented Numerics Page
http://monet.uwaterloo.ca/blitz/oon.html  Object-Oriented NA
Pointers to C++ libraries and classes.
Also see q590, "Skip Carter's Home Page".
Also see Joerg Arndt's web page on FFT code, at
q240, "Transforms (FFT, etc) and digital signal processing (DSP)"
===================================
q160.2. Math FAQ
The sci.math FAQ by Alex Lopez-Ortiz is a good reference for
many mathematical questions.  It is more oriented towards
pure mathematics than NA.
http://daisy.uwaterloo.ca/~alopez-o/math-faq/math-faq.html  Alex Lopez-Ortiz's list 
ftp://rtfm.mit.edu/pub/usenet-by-group/news.answers/sci-math-faq/  Alex Lopez-Ortiz's list via ftp
===========================================================================
q165. Books, With and Without Software, for NA
See also specific subject areas in this FAQ
at q80, "NA FAQ: Table of Contents".
Petkovsek, Marko; Wilf, Herbert; Zeilberger, Doron.  1995
   "A=B"
   Publisher: AK PETERS, Ltd., 289 Linden Street, Wellesley, MA 02181
   Telephone to (617) 235-2210.  $39.
   ISBN 1-56881-063-6
[Donald Knuth]  Science is what we understand well enough
to explain to a computer.  Art is everything else we do.
During the past several years an important part of
mathematics has been transformed from an Art to a
Science: No longer do we need to get a brilliant insight in order to
evaluate sums of binomial coefficients, and many similar formulas that
arise frequently in practice; we can now follow a mechanical procedure
and discover the answers quite systematically.
I'm especially pleased to see the appearance of this book, because its
authors have not only played key roles in the new developments, they
are also master expositors of mathematics. It is always a treat to
read their publications, especially when they are discussing really
important stuff.
Science advances whenever an Art becomes a Science. And the state of
the Art advances too, because people always leap into new territory
once they have understood more about the old. This book will help you
reach new frontiers.
Acton, Forman S.  1990
   Numerical methods that [usually] work
   Harper & Row, Publishers
   ISBN 0883854503.
[Daniel Pick] This book is almost worth its price just for the cathartic
interlude in the middle of the book on what not to compute.  You should
require your students to read it, learn it, live it.  You may find just
giving them the railroad problem found at the beginning of the book a
worthwhile exercise. [Bill Frensley] Amen, brother! The only complaint
that I have about Acton's interlude is that after demolishing the notion
of "fitting exponential data," he fails to point out that this is the
inverse Laplace transform problem.  Perhaps if everyone read this and
made the connection, we would be spared the monthly "is there any good
algorithm for the inverse Laplace transform?"
Golub, Gene H.; Van Loan, Charles F.  1989
   Matrix Computations, Second edition
   Johns Hopkins, Baltimore
   ISBN 0-8018-3739-1
   Telephone: 410-516-6900
[SJS] A classic for handling matrices.  Many current programs
are based on this text.  Good mix of theory and implementation.
Golub, Gene H.  1984
   Studies in Numerical Analysis
   Mathematical Association of America
   ISBN 0883851261.
[Daniel Pick] This contains several outstanding essays from several
numerical analysts, including Wilkinson's The Perfidious Polynomial,
which explains why rootfinding of polynomials numerically is such a
tricky problem.  It gives an great introduction to the thinking of
recent numerical analysts. [Amara Graps] All of the chapters are really
good- my favorites are: "Fast Poisson Solvers" and "Multigrid Methods
for Partial Differential Equations."
Dahlquist, Germund; Bjorck, Ake  1974
   Numerical Methods
   translated by Ned Anderson, Prentice-Hall, 1974.
A nice mix of theory and practice.
Used as a text at Stanford, among other places.[John Chandler]
Forsythe, George; Moler, Cleve B. 1967
   "Computer Solution of Linear Algebraic Systems"
    Prentice-Hall
I consider this possibly the best textbook I have ever seen
in any field.  Covers only linear systems, of course.[John Chandler]
Kahaner, David; Moler, Cleve; Nash, Stephen. 1989
   Numerical Methods and Software
   Prentice Hall, Englewood Cliffs, NJ
   ISBN 0-13-627258-4
   Telephone: 800-947-7700
An excellent book which touches on a variety of topics and makes
use of the publicly available software like the QUADPACK and SLATEC
libraries to illustrate the points. [Vijay Gupta]
Knuth, Donald E. 1981
   Seminumerical algorithms, 2nd edition.
   Addison-Wesley.
Once was the reference; now a bit dated.
Lau, H. T. 1995
   A Numerical Library in C for Scientists and Engineers
   CRC Press, Boca Raton, FL
   ISBN 0-8493-7376-X
   Telephone: 407-994-0555
This book is basically a compilation of program listings,
with a diskette containing source code.  The listings
are accompanied by brief overviews of the algorithms
involved, and generally include references.  There is
no discussion of theory.  While the text by Stoer & Bulirsch is at
the theoretical end of the NA spectrum, this text is at the
application end.  Although the program calling parameters
are well described, as far as I could see the programs
contain no internal documentation whatsoever.
Although this book is copyright 1995,
the references contain one source dated 1992 (Press et al's volume),
one source dated 1981 (NUMAL in Fortran), and one source dated
1980 (NUMAL in Algol).  The remainder of the references
are dated 1976 and earlier.  It's not clear to me that this book
offers anything over Press et al's text.  Lau has far less discussion of
theory and methodology, and while Press's internal documentation
of programs is poor, Lau's book has none whatsoever.  [SJS]
Mathews, John H.  1992
   NUMERICAL METHODS: for Mathematics, Science & Engineering
   Prentice Hall, Englewood Cliffs, NJ
   ISBN 0-13-624990-6  and
   ISBN 0-13-625047-5
   Source for the programs is available in several languages:
ftp://ftp.mathworks.com/pub/books/mathews/matlab   Matlab (ftp)
ftp://ftp.mathworks.com/pub/books/mathews/c   C (ftp)
ftp://ftp.mathworks.com/pub/books/mathews/fortran   Fortran (ftp)
ftp://ftp.mathworks.com/pub/books/mathews/pascal   Pascal (ftp)
ftp://ftp.wri.com/pub/Publications/BookSupplements/Mathews-1996/   Mathematica (ftp)
http://www.wri.com/MathSource/Publications/BookSupplements/Mathews-1996/0207-874  Mathematica (http)
Press, William H.; Teukolsky, Saul A.;  Vetterling, William A.;
   Flannery, Brian P. 1992
   Numerical Recipes in C, Second edition
   Cambridge University Press, Cambridge and New York
   ISBN 0-521-43108-5 Text
   ISBN 0-521-43720-2 Example book
   ISBN 0-521-43714-8 PC diskette, 5.25 inch
   ISBN 0-521-43724-5 PC diskette, 3.5 inch
   ISBN 0-521-43715-6 Mac diskette, 3.5 inch
   Telephone: 212-924-3900, 800-872-7423
Seperately purchasable diskette contains C source code.
A compendium of a wide variety of NA areas.  Contains some
good introductions to theory and overviews of algorithms.
The bridge from algorithm overview to implementation
is often missing.  The programs should be viewed with
some skepticism.  They are often poorly documented, and some users
have reported numerical problems with the various programs. [SJS]
Additional information may be at:
http://nr.harvard.edu/numerical-recipes  Numerical Recipes
ftp://ftp.std.com/vendors/Numerical-Recipes  Numerical Recipes via ftp
email: nr@nr.com
Some Numerical Recipes Reviews are at:
http://www.lysator.liu.se/c/num-recipes-in-c.html  N.R. Review
http://math.jpl.nasa.gov/nr  N.R. Reviews
Sedgewick, Robert. 1988
   Algorithms, Second edition
   Addison-Wesley, Reading, Mass
   ISBN 0-201-06673-4
   Telephone: 617-944-3700, 800-822-6339
Stoer, Josef; Bulirsch, Roland 1980
   Introduction to Numerical Analysis
   Springer-Verlag, New York, 1980
   ISBN 0-387-90420-4
   Telephone: 212-460-1500, 800-777-4643
The classic NA text.  A standard for graduate
and upper undergraduate courses in NA.
Difficult going, but covers a wide set of fields in depth.
Strong theoretical orientation. [SJS]
Strang, Gilbert  1988
   Linear Algebra and It's Applications, Third Edition
   Harcourt Brace, San Diego
   ISBN 0-15-551005-3
A well-written introduction to theory.
Watkins, David S. 1991
   Fundamentals of Matrix Computations
   John Wiley, New York, 1991.
   ISBN 0-471-61414-9
   Telephone: 212-850-6000, 800-225-5945
More readable than Stoer & Bulirsch or Golub & Van Loan, and contains
some implementation techniques not present in Golub & Van Loan.
Has good descriptions of theory and implementations,
and many implementations are covered as straightforward exercises.
Not as wide a variety of fields as either Golub & Van Loan or
Stoer & Bulirsch. [SJS]
Dubois, Paul.  1996
   Object Technology for Scientific Computing
   Object-Oriented Numerical Software in Eiffel and C
   Prentice Hall, 1996, paper, 350 pages
   ISBN 0-13-267808-X
   Comes with CD-ROM
   Price: $40.00 
Nash, John C., 1987, 1996
   Nonlinear Parameter Estimation: an integrated system in BASIC
   Sample chapters and portions of the code are at:
http://www.nashinfo.com/~nis/  Nash's Sample Chapters
### many others!
===========================================================================
q205. Dense (Non-Sparse) Linear Algebra Systems
The best resources for linear algebra are:
The texts by Golub & Van Loan and by Watkins.
On the net, library package LAPACK, with BLAS, from netlib
(see q115.1, "Netlib") is a widely recommended replacement
for EISPACK and LINPACK.  It handles dense matrices only.
As far as complete packages, nearly all NA packages, both on
the net and commercial, include linear algebra as part of their
core.  See the listings above.
===================================
q207. Sparse Linear Algebra Systems
Netlib (see q115.1, "Netlib") has a number of libraries
for handling sparse systems.  See the netlib directories:
sparse, sparse-blas, sparsepak.
[N. Sukumar]:
Recommends the TEMPLATES book ["TEMPLATES for the soln of linear systems:
building blocks for iterative methods"] that is availabe in postscript
format at netlib. Also in the same dir is code (in C and Fortran)
for algorithms discussed in the book.  "The book is awesome
(easy to read, good pointers on selection of solvers etc.),
especially for one who is not aware of how and why
sparse solvers work."
netlib, in the directory: templates
[N. Sukumar] also recommends:
The sparse package SPARSKIT which also has the solvers
built-in; there are many other feature in addition [matrix conversion/
formatting, plotting, statistics etc].
ftp://ftp.cs.umn.edu/.archive2/users/saad/SPARSKIT  U. Minnesota SPARSKIT
ftp://ftp.cs.umn.edu/.archive2/sparse/SPARSKIT2  U. Minnesota SPARSKIT
ftp://icarus.riacs.edu/pub/SPARSKIT  U. Minnesota SPARSKIT
===========================================================================
q210. Random Number Generators (RNGs)
	* q210.1, "Web Sites for Random Number Generators"
	* q210.2, "References for Random Number Generators"
	* q210.3, "Types of Random Number Generators"
	* q210.6.1, "Linear Congruential Generators (LCG)"
	* q210.6.2, "Add-with-carry and Subtract-with-borrow Generators (AWCG, SWBG)"
	* q210.6.3, "Multiply-with-carry Generators (MWCG)"
	* q210.6.4, "Inversive Conguential Generators (ICG)"
	* q210.7, "Tests for Randomness"
===================================
q210.1. Web Sites for Random Number Generators
pLab is an excellent web site created by the Department
of Mathematics at the Salzburg University.  It covers
RNGs and tests for randomness, and contains publications,
software, and pointers to other resources.  Use either:
http://random.mat.sbg.ac.at/  Salzburg Dept. Mathematics
http://www.mat.sbg.ac.at/home.html  Salzburg Dept. Mathematics
Additional services may be available from pLab -- see:
http://random.mat.sbg.ac.at/team pLab Overview
Another web page with info on RNGs is Skip Carter's page at Taygeta:
http://www.taygeta.com/random.html  Skip Carter's page
See also the Diehard page, described at:
q210.7, "Tests for Randomness"
Also see Pierre L'Ecuyer's papers:
http://www.iro.umontreal.ca/people/lecuyer/papers.doc L'Ecuyer
ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers L'Ecuyer ftp
Info on 1/f noise, called "flicker noise" or "pink noise", is at:
http://linkage.rockefeller.edu/wli/1fnoise   Wentian Li's site
===================================
q210.2. References for Random Number Generators
References:
V.S.Anashin. Uniformly distributed sequences over $p$-adic integers. - In:"
Number Theoretic and Algebraic Methods in Computer Science. Proc. Int'l Conf.
Moscow, June - July 1993". Alf J van der Poorten, Igor Shparlinsky and Horst G.
Zimmer - editors. Published by World Scientific, 1995.  Pp. 1 -18.
Anashin, V. S., Uniformly distributed sequences of $p$-adic integers
(Russian), Mat. Zametki 55 (1994), no. 2, 3--46, 188; MR 95f:11096 There is
an English translation of this paper made by Plenum Publ. Corp.
Anashin, V.S. Uniformly distributed sequences in computer algebra or how to
construct random number generators.  Translated from
Itogi Nauki i Tekhniki, Seria Sovremennaya Matematika i Ee
Prilozheniya. Tematicheskie Obzory, Vol.
31, Computing Mathematics and Cybernetics - 2, 1995.  1072 - 3374/96/0000 -
0001. Plenum Publisning Corp., 1996
Anashin, V. S., Solvable groups with operators and commutative rings having
transitive polynomials (Russian), Algebra i Logika 21 (1982), no. 6,
627--646; MR 85d:20028
Law, Averill M, and Kelton, W. David. 1991
   Simulation Modeling & Analysis, Second edition
   McGraw Hill, New York
Banks, Jerry.  Handbook on Simulation
   Wiley.
Bratley, P., Fox, B.L. & Schrage, L.E. 1987
   A guide to simulation, 2nd edition
   Springer
Devroye, Luc. 1986
   Non-uniform random variate generation
   Springer-Verlag, New York
[SJS] This is the most complete book I've found on generating non-uniform
random values.
L'Ecuyer, Pierre. Random numbers for simulation. Comm. ACM 33, 85-97 (1990) .
L'Ecuyer, Pierre. Uniform random number generation. 
Annals of operations research 53 (1994), 77.
Marsaglia, George. JACM 12 (1965), 83-89.
Marsaglia, George.  "Random numbers fall mainly in the planes",
Proc. Nat. Acad. Sciences USA, 61 (1968), 25-28.
Marsaglia, George.  "Remarks on choosing and implementing
random number generators",  Communications of the ACM v 36
n 7 (July 1993), p 105-107.
Marsaglia, George and Zaman, Arif.  "A new class of
random number generators".  The annals of applied
probability 1, 3, (1991), p. 462-480.
Motwani, Rajeev  and Raghavan, Prabhakar   1995
   Randomized Algorithms
   Cambridge University Press
Sullivan, Stephen.  "Another test for randomness",
Communications of the ACM 36, 7 (July 1993), p 107.
Tezuka, Hsh, L'Ecuyer, Pierre, and Couture, Raymond.
"On the lattice structure of add-with-carry and subtract-with-
borrow random number generators", ACM Trans on Modeling and
Computer Simulation 3, 4 (October 1993), p. 315-331.
Still more references, courtesy of [Ripley]:
James, F. (1990) A review of pseudorandom numbers. Comp.
Phys. Comm. 60 329--344.
Morgan, B.J.T. (1984) Elements of simulation. Chapman & Hall.
Ripley, B.D. (1983) The computer generation of random variables
- a tutorial. Int. Statist. Rev. 51 301--319.
Ripley, B.D. (1987) Stochastic Simulation. Wiley, New York
Ripley, B.D. (1990) Thoughts on pseudorandom number generators.
J. Comput. Appl. Math. 31, 153--163