Newsgroup sci.math.num-analysis 29323

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In article
 Lawrence K. Chilton, lkchilt@sgi1.math.umbc.edu
writes:
>>I am looking for a quality linear algebra library written in C which
>provides source code for each routine. Hopefully it would
>provide routines for solving Ax=b, eigensystems, etc. I am aware of
>clapack, which I use in binary form on a Linux box, but it would be very
>convenient to have modularized C source code to make the applications more
>portable. I also use the Matlab engine library, which is very nice except
>when the machine I want to use doesn't have Matlab. I would appreciate
>hearing from anyone who has a package they can recommend. I prefer a 
>public domain package, but will also consider a reasonably priced (~$100
>US) commercial library. Thanks in advance.
>
>-Larry C.
> lkchilt@math.umbc.edu
>
Matclass is one possibility. It is actually C++ code, so
maybe not. You can get it at
 http://les.man.ac.uk/ses/staff/crb/matclass/
Another possibility is Meschach. It is C code, available
for most everything. To find it, do a search on any of the
search engines for the name meschach. You'll get plenty of
hits.
I have ported both of these to the macintosh, if you are a
mac user.
Mike Yukish
Applied Research Lab
may106@psu.edu
http://elvis.arl.psu.edu/~may106/

Mike Yukish wrote:
> 
> In article
>  edu> Lawrence K. Chilton, lkchilt@sgi1.math.umbc.edu
> writes:
> >>I am looking for a quality linear algebra library written in C which
> >provides source code for each routine. Hopefully it would
> >provide routines for solving Ax=b, eigensystems, etc. I am aware of
> >clapack, which I use in binary form on a Linux box, but it would be very
> >convenient to have modularized C source code to make the applications more
> >portable. I also use the Matlab engine library, which is very nice except
> >when the machine I want to use doesn't have Matlab. I would appreciate
> >hearing from anyone who has a package they can recommend. I prefer a
> >public domain package, but will also consider a reasonably priced (~$100
> >US) commercial library. Thanks in advance.
> >
> >-Larry C.
> > lkchilt@math.umbc.edu
> >
> 
> Matclass is one possibility. It is actually C++ code, so
> maybe not. You can get it at
> 
>  http://les.man.ac.uk/ses/staff/crb/matclass/
> 
> Another possibility is Meschach. It is C code, available
> for most everything. To find it, do a search on any of the
> search engines for the name meschach. You'll get plenty of
> hits.
> 
> I have ported both of these to the macintosh, if you are a
> mac user.
> 
> Mike Yukish
> Applied Research Lab
> may106@psu.edu
> http://elvis.arl.psu.edu/~may106/
It may be difficult to find a more mature product than LAPACK. Why don't
you get the C source code from netlib? All you have to do is to install
the f2c-libs available at netlib also and you can keep using the same
calls etc you are using right now. If you wnat to be able to use
everything in CLAPACK get everything, otherwise there is the possibility
to get routines with dependencies. Also, you may need the BLAS in case
you can't (preferably) use the built-in ones on your platform.
-- 
Hans D. Mittelmann			http://plato.la.asu.edu/
Arizona State University		Phone: (602) 965-6595
Department of Mathematics		Fax:   (602) 965-0461
Tempe, AZ 85287-1804			email: mittelmann@asu.edu

Nablus
                An-najah Natonal University
The department of Mathematics at An-Najah National University in Nablus
- PALESTINE invites applications for faculty positions in th fields of
(1) Partial Differential Equations
(2) Numerical Analysis
starting october 1,1997. Yhe completed doctorate is required and/or
research experience required.
The department offers both Bachelor's and Master's degree.
Candidateswill be expected to engage in research,teach both graduate
and undergraduate levels, snd to be qualified to supervise student 
research and thesis writing.
Applicants should send a letter of application,transcripts,
a cirriculum vitae and three letters of reference to be sent before 
June 1, 1997   
                    Department of Mathematics
                    An-Najah National University
                    Nablus
                    Palestine.
		    Email: alamleh@najah.edu

Lawrence K. Chilton wrote:
> 
> I am looking for a quality linear algebra library written in C which
> provides source code for each routine. Hopefully it would
> provide routines for solving Ax=b, eigensystems, etc. I am aware of
> clapack, which I use in binary form on a Linux box, but it would be very
> convenient to have modularized C source code to make the applications more
> portable. I also use the Matlab engine library, which is very nice except
> when the machine I want to use doesn't have Matlab. I would appreciate
> hearing from anyone who has a package they can recommend. I prefer a
> public domain package, but will also consider a reasonably priced (~$100
> US) commercial library. Thanks in advance.
>  
> -Larry C.
>  lkchilt@math.umbc.edu
Sorry for mailing my previous response to the first replier instead of
the originator. Read it in the newsgroup, please. Also, if you work on a
Linux box you don't need to install the f2c-libs, they are probably in
/usr/bin, so you can just say -lf2c. You may need to just install
libblas.a, also from netlib.
-- 
Hans D. Mittelmann			http://plato.la.asu.edu/
Arizona State University		Phone: (602) 965-6595
Department of Mathematics		Fax:   (602) 965-0461
Tempe, AZ 85287-1804			email: mittelmann@asu.edu

*SIGH*
BLStansbury  wrote:
>>
>>	No, not quite.  If we want to write pi down in some 
>>positional notation (i.e., decimal) or use it in computation, 
>>THEN we must approximate it.
>Oh, so we do not approxiamte it at other times. I did not realize
>this.
	Correct.  We only approximate PI when doing real-world 
computation with it.  In mathematics, we use its exact value.
>>	It is a lie that the best one can do is approximate.  
>>Mathematics is exact
>I understand. Could you please send me the exact value of pi.
	Sure.  How about 6*arcsin(1/2)?  See, Mr. Stansbury, I
think you are not apprehending the distinction between the VALUE
of a constant and its decimal representation.  Decimal 
representations are things we write down, and do arithmetic with.
But while PI can be written as "approximately 3.14159...," that 
is not the value of PI, any more than the name "Mr. Stansbury"
*is* Mr. Stansbury.
	Imagine that, one day, I decide to change my last name
to an infinitely long string, whose letters form no recognizable
pattern.  You then have me, Scott Craverthreepointonefouronefive...
and the actual name "Scott Craverthreepointonefouronefive...."
You'll never write my name down completely [lots of fun at 
graduation!] but that's just a name.  If you respond to "I 
bumped into Scott Craverpi the other day" with, "NO YOU DIDN'T!!  
YOU JUST BUMPED INTO AN APPROXIMATION OF Scott Craverpi!!", then
you are probably not clear on the use-mention distinction, 
between the name of something and its value.  This is what you 
seem to be displaying here.
	We will never be able to do base-10 arithmetic with the
exact value of PI, because we would have to write PI in base-10,
which would require an infinite number of digits.  But mathematics
IS NOT COMPUTATION.  We use the exact value of PI in mathematics.
We just don't restrict ourselves to writing answers entirely in
decimal, get it?  A circle of radius 2 has area 4pi, exactly. 
>1/3 * 300 = 100   and   100/pi * pi = 100
>1/pi * 3.14159265359... does not = 1
	I assume that by "3.14159265359..." you mean only a finite
number of digits, yes?  Sure, then.  But what does that show?
1/(1/3) * 0.33333333333 does not = 1 either.  Again, just because
we can't write it in base-10 doesn't mean we can't use its exact
value.  Similarly, just because we can't draw a perfect circle 
doesn't mean we can't use perfect circles in mathematics.
>>	Um, no.  What we can do in mathematics does not depend
>>on how many digits of PI a machine can crank out, or how sharp a 
>>pencil we can build.
>?
	Do you want me to elaborate on this?
>> The squaring a circle is impossible even 
>>with perfectly accurate tools [meaning, of course, an unmarked
>>straightedge and compass].
>Or by any other means.
	Not true.  Squaring the circle *is* possible if we 
slightly modify those perfectly accurate tools.  With an umarked
straightedge and collapsing compass, it cannot be done.
>BLS
 ,oooooooo8     o     ooooo@math.niu.edu  --  http://www.math.niu.edu/~caj/
o888'   `88   ,888.    888                                                 
888          ,8'`88.   888  "This year's Summer fasions are simple yet
888o.   ,oo ,8oooo88.  888   vibrant, as I will prove using the following
`888oooo88 o88o  o888o 888   lemma."  -Cindy Crawford, _Gauss_of_Style_
____________________8o888'_________________________________________________

Jonathan Thornburg wrote:
> 
> In an article to which I have alas lost the reference :=(,
> Lars Marius Garshol  asked about numerical methods
> for a celestial mechanics simulation, i.e. for integrating the ordinary
> differential equations (ODEs) of motion of bodies under gravity.
> 
> In article ,
> Henry Spencer  wrote
> 
> | [various excellent advice on better numerical methods deleted]
> |
> | The state of the art is Richardson
> | extrapolation, e.g. the Bulirsch-Stoer method, which takes a series of
> | successively better (but successively more costly) estimates and
> | extrapolates the series to infinity.
> 
> The Bulirsch-Stoer method is an important one (and certainly orders of
> magnitude better than the Euler method Lars Garshol appears to be using),
> but Bulirsch-Stoer isn't the state of the art in ODE integration.  I'm
> not an ODE expert, but review papers by people who *are* experts in this
> field, eg
> 
>         C. W. Gear
>         "Numerical Solution of Ordinary Differential Equations:
>          Is There Anything Left To Do?"
>         SIAM Review 23(1), Jan 1981, pp.10-24
> 
>         George D Byrne and Alan C Hindmarsh
>         "Stiff ODE Solvers: A Review of Current and Coming Attractions"
>         Journal of Computational Physics 70(1), May 1987, pp.1-62
> 
> make it pretty clear that Runge-Kutta and Predictor-Corrector methods
> are generally preferred.
Henry's claim about the Bulirsch-Stoer method (which should be referred
to as the Gragg-Bulirsch-Stoer (GBS) method in light of Gragg's seminal
paper Siam J. Numer. Anal., Ser. B, vol. 2, pp. 384--403) is an example
of what happens when you get your (mis)information from NR.  The first
edition's discussion of numerical ODEs is pretty bad.  Shampine
mentioned some of the problems in his review, but there are others.  For
example, the first "example" of a stiff problem is really unstable (not
stiff).  Fortunately the authors switched to an example by Gear (that is
stiff) before doing any analysis on a problem per se.  This distinction
between stiffness and instability is often unappreciated by laymen, who
tend to assume that any difficult problem is "stiff."  The difficulty
with a stiff problem is that, in effect, it is TOO stable for explicit
methods (and many implicit ones).  Moreover, a method appropriate for
stiff problems (e.g. BDF) is probably the LAST thing you'd want to use
on an unstable problem (ask me and I'll explain why).  
I agree that the second edition of NR is much better.  The problem is
that a novice needs an introduction he can trust, and you can't trust
NR.  It's rather unsatisfying to recommend a book that is so uneven, but
it has its merits, and, as you say below, it is practically the only one
of its kind.
FYI:  ODEPACK is good, but I think that VODE (familiar authors:  Brown,
Byrne, Hindmarsh -- see http://www.netlib.org/ode/) is generally more
efficient, except that there are variations in ODEPACK that I don't
think have been implemented for VODE, e.g. automatic switching between
BDF and Adams methods based on stiffness detection.  It is easier (less
expensive) for VODE to change the step size, and it makes more efficient
use of Jacobian evaluations.
> NR, but give better advice and much *much* better codes.  Alas, I don't
> know of any 1-volume numerical analysis surveys that are as accessable
> to the beginner as NR, cover as broad a range as NR, and are written
> by experts in the field.
Nor do I.  Such a book is possible, but it needs an organizer to make it
a reality.  For example, I think Shampine could write a few great
chapters on solving ODEs.  Check out his articles on "The Saavy Solver"
in the C*ODE*E newsletter (http://www.math.hmc.edu/codee/home.html --
somewhere in the back issues).  This kind of gentle introduction
followed by more technical information and free, polished mathematical
software would be great for the uninitiated.  I'm sure there are experts
in other areas who can do the same -- you'd probably end up with 20
authors or more.  But, alas, who will make it happen?  Who can?
-- 
Mike Hosea (mhosea@ti.com)	Texas Instruments Inc.
phone	(972) 917-2958		PO Box 650311, MS 3908
fax	(972) 917-7103		Dallas, TX  75265

On Tue, 31 Dec 1996 04:38:43 GMT, juanvp@impsat1.com.ar (JuanVP)
wrote:
If I ask 100 of my students to give me the area of a pi x pi square,
and each one of them gives me a right but different answer, which
value(s) should I accept? All of them right? And none of their answers
would be exactly the same.
BLS

On Tue, 31 Dec 1996 23:28:37 GMT, bstan@datasync.com (BLStansbury)
wrote:
>On 31 Dec 1996 18:40:25 GMT, caj@sherlock.math.niu.edu (Xcott Craver)
>wrote:
>
>>Sure.  How about 6*arcsin(1/2)?
>Approximation to pi.
No, it's the real McCoy. :)
>> If you respond to "I 
>>bumped into Scott Craverpi the other day" with, "NO YOU DIDN'T!!  
>>YOU JUST BUMPED INTO AN APPROXIMATION OF Scott Craverpi!!", then
>>you are probably not clear on the use-mention distinction, 
>>between the name of something and its value.  This is what you 
>>seem to be displaying here.
>Cute.
Yes, isn't it? I enjoyed this very much.
>>We just don't restrict ourselves to writing answers entirely in
>>decimal, get it?  A circle of radius 2 has area 4pi, exactly. 
>But a square can't have an area of exactly 4pi unless its a circle.
Is this a flame bait or just a lapsus?
>>Again, just because we can't write it in base-10 doesn't mean we
>>can't use its exact value.
>You can't write its exact value in any base.
How about in base Pi? It would be 10, wouldn't it?
Juan

PRIMAL-DUAL INTERIOR-POINT METHODS by Stephen J. Wright
SIAM 1997 / xx+289 pages / Softcover / ISBN 0-89871-382-X / Order Code
OT54
For more information please see
http://www.siam.org/books/swright/
Contents:
Preface
Notation
Chapter 1: Introduction
Chapter 2: Background: Linear Programming and Interior-Point Methods
Chapter 3: Complexity Theory
Chapter 4: Potential-Reduction Methods
Chapter 5: Path-Following Algorithms
Chapter 6: Infeasible-Interior-Point Algorithms
Chapter 7: Superlinear Convergence and Finite Termination
Chapter 8: Extensions
Chapter 9: Detecting Infeasibility
Chapter 10: Practical Aspects of Primal-Dual Algorithms
Chapter 11: Implementations
Appendix A: Basic Concepts and Results
Appendix B: Software Packages
Bibliography
Index
In the past decade, primal-dual algorithms have emerged as the most
important and useful algorithms from the interior-point class. This
book presents the major primal-dual algorithms for linear programming
in straightforward terms. A thorough description of the theoretical
properties of these methods is given, as are a discussion of practical
and computational aspects and a summary of current software.
Steve Wright
MCS Division
Argonne National Laboratory