Newsgroup sci.math.num-analysis 28605

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The trading arm of a major investment firm is seeking a quantitative
specialist for its New York based Analytical Equity Trading Group to
work with its senior professionals in the on-going development of
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Please reply via email with either a resume or a short informal
description of yourself.  Please include a day & evening phone number.  
We are an Equal Opportunity employer.

Hi,
I am seeking a Fortran (C) code for estimating an ARMA model for a
multivariate process.
Any hints welcome.
	Gerd

Hi,
I am seeking a Fortran (C) code for estimating an ARMA model for a
multivariate process.
Any hints welcome.
	Gerd

In , Octavio Hector Juarez Espinosa  writes:
>Hi,
>
>I would like to know if there are some routines in "C" or any language
>to read a matrix from disk.
>I am reading element by element (519 by 519) and delays 11 minutes.
>In a PC with visual basic delays 35 minutes. I would like to know if there
>are ways to speed up the process?
>Thanks,
>
>Octavio Juarez
Octavio,
A few things to consider:
1. Use a "32 bit" compiler if you are not already doing so.
2. Use a disk cache if you are not already doing so.
3. If you already doing each of 1 and 2, try a fortran compiler, a
32 bit one of course.
Jerry

Miroslav Trajkovic  writes:
>I have one problem which looks very nice but I am not sure if it
>has nice solution.
>Let a = [1 p q r s]',  //where ' means transpose
>    b = [1 u v w z]'
>and A = a*a';
>Is there anu "shortcut" to solve the system
>A*x = b;
Well, I'm really just learning linear algebra, but it looks to me like
you can definitely tell if this problem has solutions, and what they
are, pretty easily.  The problem is that aa' is a rank 1 matrix. 
Anyway, I played with actually doing the problem out, but then I thought
of this:
aa'x = b
a(a'x) = b
(a'x)a = b
So, this trivially says that a dot x (otherwise known as a'x) times a
has to equal b.  Now, the bummer for you is that the first element of a
and b are equal, so it looks like a'x has to equal 1, and a and b have
to be equal as well, or else there's no solution.  If a'x=1 and a=b then
you've got a family of solutions that satisfy a'x=1.
I hope I'm not missing something.
Chris

Octavio Hector Juarez Espinosa wrote:
> 
> Hi,
> 
> I would like to know if there are some routines in "C" or any language
> to read a matrix from disk.
> I am reading element by element (519 by 519) and delays 11 minutes.
	Well don't read one element at a time - read a larger chunk
of data with each disk read.
> In a PC with visual basic delays 35 minutes. I would like to know if there
> are ways to speed up the process?
	Don't ever use VB for anything. Borland Delphi is just as 
convenient as VB but much faster.
-- 
David Ullrich
?his ?s ?avid ?llrich's ?ig ?ile
(Someone undeleted it for me...)

I found a formula for computing PI numerically, but it takes a LONG time
to converge.
Here is the formula:
         2*2*4*4*6*6*8*8...
PI = 2*----------------------
         1*3*3*5*5*7*7*9...
However, when put into a computer, it takes a long time to converge.
Even after a billion iterations, it only has 10 or so digits.
Can anyone give me a formula that I can put into the computer and have
it converge fairly quickly?  Is it possible?
I want something that will give a more precise answer if the computer
has longer time to process it.
Thanks,
- Mark
(please e-mail me your responses as I don't check this list often.)

In article , "M.A. Cremonini"  writes:
|> 
|> 
|> Hi,
|> I must solve a problem like this:
|> 
|> 		Ax=B
|> 
|> A is my data matrix ans B is a column vector with results.
|> B is formed by numbers which can span a certain range i.e. all
|> the numbers within
|> the range can be solutions of the corresponding equation:
|>         
|>         |a11  a12| |x1|     |B1 +/- e1| 
|>         |a21  a22| |  |  =  |B2 +/- e2|
|>         |a31  a32| |x2|     |B3 +/- e3|
|>         |a41  a42| |  |     |B4 +/- e4|
|> 
|> For example:
|>               
|> if A11*x1+A12*x2 = Q and Q is within the range (B1-e1 - B1+e1) the result
|> is the one searched for.  
|> 
|> 
snip snip  ..
if your errors in the right hand side are of statistical nature , 
stochastically independent, with mean zero and the same variance
then solving the normal equations would give a correct estimator 
(but normally, you should have much more observations than just 4 for 4
unknowns!). As a matter of fact, as you indicate, the variances of the
right hand sides components are not equal,  hence you must use
appropriate weighting. the normal equations are
A(transpose)Ax = A(transpose)B
If this system comes from some other source, it may be more useful 
to use interval arithmetic to solve for the solution set or a bound of it.
see the books of moore or alefeld and herzberger for an introduction 
to interval analysis.
hope this helps
peter

Subject: Special Issue of the International Journal of Applied Science 
	  and Computation
The International Journal of Applied Science and Computation will be 
publishing a special issue edited by David Schultz and Bruce Wade on 
computational fluid dynamics.  Any topics related to this area will be 
considered for publication.  
Requests for additional information can be addressed to schultz@math.uwm.edu. 
Contributors should send three copies of their paper to:
                   David Schultz, Professor
                   Department of Mathematical Sciences
                   University of Wisconsin-- Milwaukee
                   PO Box 413
                   Milwaukee, Wisconsin  53201-0413
-- 
Bruce A. Wade, Associate Professor, Dept. of Mathematical Sciences
University of Wisconsin-Milwaukee, TEL: (414) 229-5103, FAX: (414) 229-4907
E-MAIL: wade@csd.uwm.edu, WWW: http://www.math.uwm.edu/
Amateur Radio: N9UR

In article <560vs6$67u@prometheus.acsu.buffalo.edu>, v075t2l4@ubvms.cc.buffalo.edu writes:
|> Hi, 
|> is there anybody who is familiar with the software that solves two point
|> boundary value problems arising from the application of Pontriagon's
|> maximum (or minimum) principle in the field of optimal control. There is
|> a state dynamics with state and control (input) inequality constraints.
|> The program should be robust and can handle nonlinear system of differential
|> equations. Anybody can help me is higly appreciated. Thanks
try bvpsol from elib/codelib 
telnet elib.zib-berlin.de
login as elib --- no password required 
follow the decison tree to codelib and retrieve bvpsol then.
hope this helps
peter

The sci.math FAQ has a spigot algorithm written by Dik Winter
that will compute a large number of digits quickly.  If you want
to calculate millions of digits, do a web search for PI and AGM
or a search for MPFUN.  If you want to calculate billions of
hexadecimal digits, there is an algorithm that will calculate
any hex digit of pi.  You might also try the inverse symbolic
calculator page, or Eric's Treasure Trove of Mathematics.
Mark Gardner  wrote in article <32889816.167E@cc.usu.edu>...
> I found a formula for computing PI numerically, but it takes a LONG time
> to converge.
> 
> Here is the formula:
> 
>          2*2*4*4*6*6*8*8...
> PI = 2*----------------------
>          1*3*3*5*5*7*7*9...
> 
> However, when put into a computer, it takes a long time to converge.
> 
> Even after a billion iterations, it only has 10 or so digits.
> 
> Can anyone give me a formula that I can put into the computer and have
> it converge fairly quickly?  Is it possible?
> 
> I want something that will give a more precise answer if the computer
> has longer time to process it.
> 
> Thanks,
> 
> - Mark
> 
> (please e-mail me your responses as I don't check this list often.)
> 

In article <01bbd065$231f9fd0$2dac399d@a-cnadc1>, "Dann Corbit"
 wrote:
> The points often, but not always, converge to the zero of
> the function.  The problem you describe was investigated
> by one B. Mandelbrot.
            ^^^^^^^^^^^H^H^H^H^H^H^H^H^H^HCayley

In article <3286E56D.3A5F@sas.seismology.hu>,
Zoltan Bus   wrote:
>Hi!
>
>Somebody, please, define me what is the meaning of the expression
>'leading dimension' which can be found in almost FORTRAN matrix
>subroutine. Excuse me for this silly question.
>
>Thank you very much
>
>Zoltan Bus
The leading dimension is the actual size the first column of a matrix is
dimensioned to.  It's a little more clearer if I just use an example:
      dimension A(13,20)
C fill only the 4x4 part of A
      do 100 i=1,4
      do 100 j=1,4
        A(j,i) = i*j
  100 continue
...
C the leading dimension of A = 13
C the dimension of the data in A = 4
      call something(A,13,4)
...
      end
      subroutine something(Array,NLA, NA)
      dimension Array(NLA, NA)
...
Fortran is column-major, or in other words, successive columns of an array
are stored in memory.  In the above example the memory location A(1,2)
follows immediately after A(13,1).
The subroutine "something" needs the leading dimension so that it can
find all the elements of the 4x4 array stored in A.
Hope this is helps.
	R.K.
+-------------------------------+------------------------------+
| R.K.Owen,PhD                  | rk@owen.sj.ca.us             |
| LBNL/NERSC                    | rkowen@nersc.gov             |
| Univ. of California, Berkeley | Wrk:(510)486-7556            |
+-------------------------------+------------------------------+

Hi,
I just read a paper where they solved the NLSE by a
split-step spectral method.  The NLSE is
       dU         h^2 
 ih  -----  = - ------ grad^2 U + (v|U|^2 + w)U
       dt          2m
and the method described solves the non-linear part in
real-space and the Laplacian oprerator in Fourier space.
Where can I find information on this method?
Thanks,
George Klinich
klinich@mps.ohio-state.edu

In article <32827F30.4F0F@asu.edu> "Hans D. Mittelmann"  writes:
> Iterative methods are applied when the matrix is sparse. It is not by
> itself generally an advantage for these methods that it is banded.
Depends on your band width. The matrix from central differences / 
linear elements on a square grid is banded and sparse. The bandwidth
is so large, however, that you do not make any use of htat fact.
To the original poster: what exactly is the size of the band?
O(1)? Or O(sqrt(N))?
Victor.
-- 
405 Hilgard Ave ...................... The US pays 120,000 rubles rent on its
Department of Mathematics, UCLA ........... Moscow embassy. At the signing of
Los Angeles CA 90024 ........................... the lease this was $170,000,
phone: +1 310 825 2173 / 9036 ....................... today it's about $22.56
http://www.math.ucla.edu/~eijkhout/                        [source: Sevodnya]

In article <567nn3$4s1@newstand.syr.edu>, Tom Scavo  wrote:
>Hi,
>
>Anyone who has studied Newton's method on the real line knows its 
>geometric interpretation, that is, a sequence of tangent lines whose 
>zeros converge to a root of a function.  What is the corresponding 
>geometric interpretation of Newton's method in the complex plane?
>
>Explanations or pointers into the literature will be most appreciated.
>If you post, please cc trscavo@syr.edu as well.
 Before it becomes tangled in the intricacies of fractals, let me sum up 
the "good news":
 Newton's method in many variables works with the Jacobian matrix and its 
inverse. For two variables, we try to solve
   f_1(x_1,x_2)=0
   f_2(x_1,x_2)=0     ... in vector form, f(x)=0.
 Taylor's expansion around x, with first order derivatives, is
   f(x+h) = f(x) + J(x) * h + R(h)
 where J(x) = [partial f_1/partial x_1   partial f_1/partial x_2]
              [partial f_2/partial x_1   partial f_2/partial x_2]
and the remainder R goes to 0 faster than ||h||.
 If you neglect the remainder, you obtain the linear (some prefer 
"affine") approximation to f(x+h) by f(x) + J(x)*h.
 Assuming that J(x) is invertible, we try to improve x by solving
   f(x) + J(x)*h = 0, and declare x+h to be a new guess. This gives us
  x+h = x - (J(x))^(-1) * f(x)
 In one variable, this is Newton's method, isn't it? It assumes that 
f'(x) is not 0, of course. And if f has bounded second order partial 
derivatives and a bounded inverse of the Jacobian matrix in a 
neighbourhood of the exact solution then guesses sufficiently close to 
the exact soution lead to a "quadratically convergent" sequence, it is, 
the present error is bounded by a constant multiple of the square of 
the previous error. Like in one real variable.
 Now for the analytic functions: for z = x_1 + i * x_2,
  f(z) = f_1(x_1,x_2) + i * f_2(x_1, x_2)
and the Jacobian matrix J(x) acts on [h_1,h_2]' the same way as the 
complex number f'(x) on h_1 + i * h_2 (up to obvious notational changes). 
The reason is Cauchy-Riemann equations
   partial f_1/partial x_1 =   partial f_2/partial x_2
   partial f_1/partial x_2 = - partial f_2/partial x_1
valid whenever f is analytic.
(Check out the algebra!)
Then the formula  x_new = x - f(x)/f'(x)
is a consequence of the more general two-variable method.
Remark: Even in one variable, you can get pathological cases:
Solving x^3-5*x=0, starting with x_0=1, leads to a cycle 
 {1, -1, 1, -1, ...} 
which is unstable (will depart from cycling if you start from numbers 
close to 1 but different from 1)
and solving x^3 - 2*x + 2 = 0 (Smale's example), starting from 0, leads to
a stable cycle {0, 1, 0, 1, ...}. Experiment with x_0 from [-0.1, 0.1]. 
Good luck, ZVK (Slavek).

Fred,
This is interesting.  Do you know if Microsoft has plans to add these
improvements to Visual C++?  What about Borland C++?  Does Borland
implement a long double as real10?
Stephen
tydeman@tybor.com wrote in article <5699a2$12k@gate.seicom.net>...
> In <3286B63E.5BB6@WorldNet.att.net>, "Jeffery J. Leader"
 writes:
> >Kahan gave an interesting talk on this type of thing at the Gragg
> >Conference in Monterey last weekend--all the directed rounding,
> >overflow/underflow, etc. stuff that's built into the chips but not
> >reasonably accessible from most compilers.  Interesting but frustrating.
> 
> C9X, the revision of C currently under way, has added the Floating-Point 
> C Extensions (FPCE) that will enable a numerics programmer to get access
> to the floating-point environment which includes the rounding direction
> and the exception flags.  Several compiler vendors already support FPCE.
> 
> Fred Tydeman          +49 (7031) 288-964  Tydeman Consulting
> Meisenweg 20          tydeman@tybor.com   Programming, testing, C/C++
training
> D-71032 Boeblingen                        Voting member of X3J11 (ANSI
"C")
> Germany               Sample FPCE tests: 
ftp://ftp.netcom.com/pub/ty/tydeman
> 
> 

There's also a web site with a demonstration linking
fractals to Newton's method:
http://www.ma.iup.edu/projects/CalcDEMma/newton/newton.html
Dann Corbit  wrote in article
<01bbd066$bcd0c220$2dac399d@a-cnadc1>...
> I should mention that there is software that will draw
> nice pictures of the geometric interpretation.  Do a web
> search for 'fractint' to find it.

In Japan, many researchers pronounce LaTeX as "latef." Is it correct? How do you 
pronounce TeX and LaTeX actually, especially in the united states?

Are you interested in solving the wave equation numerically?
If so you might want to consider two time domain methods:
- finite difference time domain
- finite element time domain
You might also consider the possibility of going to a system
of first order equations, as the numerical results are more stable.
Regards,
Dragos Bica
==========A Montvay {TRACS}, 11/4/96==========
Hi all,
I want to use a Runge-Kutta (or similar) method on an IBVP on the
three-dimensional wave equation
d2p/dx2+d2p/dy2+d2p/dz2-d2p/dt2=0
Most books on numerical solutions of DE describe Runge-Kutta for ODE
some transfer it to first-order PDEs in two dimensions, but i have
not found any for second order in four dimensions.
Therefore any algorithm, program code in (almost)any language,
reference to book/paper or hints on how to do it myself would be very
welcome.
I hope somebody helps me so I don't have to figure it out myself -
after all I'm sure this has been done before!
Andras

Hello,
I was wondering if someone could answer a question from a
non-math.num.analysis guru:
I would like help in finding software which will provide model coefficients
to correct a single dependent variable for three independent variables, one
of which is a derivative-of-time of one of the other independent variables.
Is what I am trying to do called "multiple regression"?  If not, what is
the term for this class of problems?
For solving this problem, what package would best for someone who is not a
math expert?
I'd prefer freeware or shareware for Win32/Win16/DOS (in order of
preference), but would pay for a low-cost package if I could gain
user-friendliness.
Please note that it is a *must* that the software handle the
derivative-of-time variable.
Any advice would be appreciated.  I'll post a summary of responses.
Thanks,
rah@cris.com

Mark Leung (mleung@silver.ucs.indiana.edu) wrote:
: Does anyone know if there is any computer package for
: running kernel regression (or parzen window estimation)?
: Thanks.
: Mark
I am also interested in this.  Especially if anyone knows
if there is any computer package for running multivariate
kernel regression.  My email address is:
finasc@ccunix.ccu.edu.tw
thanks.
Ansing

Hideo Hirose  writes:
> In Japan, many researchers pronounce LaTeX as "latef." Is it correct? How do you 
> pronounce TeX and LaTeX actually, especially in the united states?
The question has already been adressed by Donald Knuth himself, who
explained that the X in "TeX" is actually the Greek letter chi, and
therefore should be pronounced like "chi" in Greek, "ch" in German,
Irish, or Scottish, or like the corresponding sounds in Russian,
Arabic, etc. That seems to be too difficult for most speakers
of English, so what I hear in practice is either "tek" (in analogy
to the English pronunciation of words like "technical") or "tex",
especially "latex", i.e. totally ignoring the intended etymology.
-- 
-------------------------------------------------------------------------------
Konrad Hinsen                          | E-Mail: hinsen@ibs.ibs.fr
Laboratoire de Dynamique Moleculaire   | Tel.: +33-76.88.99.28
Institut de Biologie Structurale       | Fax:  +33-76.88.54.94
41, av. des Martyrs                    | Deutsch/Esperanto/English/
38027 Grenoble Cedex 1, France         | Nederlands/Francais
-------------------------------------------------------------------------------

as I remember it can be found in  Press et al. : Numerical Recipes
best regards
Zoltan

Hello there
Anyone of you has references/code for chebychev approximation of
functions f(x,y)? Approximation of continuous functions f(x) is
quite easy, and I think the two dimensions problem should look 
like it...
Thank you
PS: Please, answers by e-mail too...
--
                   ```
                  (o o)
--------------oOO--(_)--OOo--------------------------------------------------
Francesco P. Lovergine | E-mail: lovergine@iesi.ba.cnr.it    |I stituto
CNR-IESI               | WWW: http://www.ba.cnr.it/~iesifl01 |E laborazione
Via Amendola 166/5     | Pho: +39 80 5481969 5481612 5481699 |S egnali e
70126 Bari             | Fax: +39 80 5484311                 |I mmagini
I T A L Y              |                                     |
-----------------------------------------------------------------------------
       Nessuna impresa e' mai stata compiuta da un uomo ragionevole.
-----------------------------------------------------------------------------

Octavio Hector Juarez Espinosa (oj22+@andrew.cmu.edu) wrote:
: I would like to know if there are some routines in "C" or any language
: to read a matrix from disk.
: I am reading element by element (519 by 519) and delays 11 minutes.
Are you obligued to use a given format in that the matrix is stored
on disk? If not, check if your matrices are "sparse", i.e. most
entries are zero. In this case, you only have to write the
non-zero elements to disk, together with their position, i.e. you
have to write (and later to read) a sequence of triplets (i,j,a).
So writing and reading a matrix should be much faster.
: In a PC with visual basic delays 35 minutes. I would like to know if there
: are ways to speed up the process?
I'd suggest using a _programming language_ instead of VB ;->
(Forgive me, but I couldn't resist giving this silly remark ;-)
Greetings,
                                       Andreas Jung.
--
Andreas Gisbert Jung     DL9AAI Tel:0381/498-3364 Fax:0381/498-3366
Theoretische Informatik  mailto:ajung@informatik.uni-rostock.de
Universitaet Rostock     http://www.informatik.uni-rostock.de/~ajung/
PGP fingerprint =  8A 0B 05 CA EE AB 7B 01  D9 07 6A D0 84 38 BB 82

Hi,
Is there any free (or almost free) software available (preferably
source code) to calculate the thermodynamic properties of steam and
water?
I have found several places that charge $200 and up. I just want this
for entertainment and can't justify that kind of $$.
Thanks
Mike Johnston

> The question has already been adressed by Donald Knuth himself, who
> explained that the X in "TeX" is actually the Greek letter chi, ...
	A greek colleague of mine says "tej", but in america everybody
I know call it "tek".
-- 
Federico Waisman
School of Civil and Environmental Engineering  
Cornell University                             email: fmw1@cornell.edu
Ithaca, NY 14853                  http://www.cee.cornell.edu/~federico

See the book "Nonlinear Fiber Optics" by G. P. Agrawal (Academic Press)
for a brief description, plus references.  He uses the split-step
Fourier method for solving the NLSE describing optical soliton
evolution.  You might also want to consider a finite-difference,
real-space type method.
-- 
Stephen R. Chinn, Optical Communications Technology
MIT Lincoln Laboratory
M/S C-280,  244 Wood Street
Lexington, MA 02173-9108
PHONE: (617) 981-5370;		FAX: (617) 981-4129

root (root@trev.seismology.hu) wrote:
: as I remember it can be found in  Press et al. : Numerical Recipes
: best regards
: Zoltan
Numerical recipes has algorithms for non-power-of-two numbers of points
but not nonequispaced points.  Nonequispaced points is tough.  There are
two options:
1. Use some interpolation technique to obtain equispaced points.  Cubic
spline interpolation works well only if the error in each Y value is 
usually smaller than the delta Y to the adjacent points.  I've used a
different interpolation technique: a time domain convolution with a
gaussian.  This limits the high-frequency portion of the spectrum.
2. Use a SFT (Standard Fourier Transform) implemented with some numerical
integration technique.  This is very robust and gives the most accurate
results.  It is slower than the FFT for large data sets, but you can save
a lot of time by only performing the calculation for the frequency range of 
interest.  I've used this technique extensively with excellent results.
--
Michael Courtney, Ph. D. 
michael@amo.mit.edu