HDTenEightyP/NetNews huggingface dataset:
From: cachoo@lincoln.ac.nz
Newsgroups: sci.math.num-analysis
Subject: SUMMARY: Minos/GAMS address
Date: 22 Dec 92 21:44:16 GMT

Thanks to everyone who replied to my query, here are the details for
those interested. GAMS and MINOS can be obtained from:
--------------------------------------------------------
>	The Scientific Press
>	651 Gateway Boulevard, Suite 1100
>	South San Francisco, CA 94080-7014
>
>	415-583-8840
> 415-583-6371 (fax)
> 70742.555@compuserve.com
----------------------------------------------------------
From: pa@verano.sba.ca.us (Pierre Asselin)
Newsgroups: sci.math.num-analysis
Subject: Re: Nonlinear systems of equations
Date: 24 Dec 92 02:18:04 GMT
Organization: None.  Santa Barbara, CA

In <1992Dec22.044947.17093@mel.dit.csiro.au>
	amal@mel.dit.csiro.au (Amal De Silva) writes:

>One method of solving this problem is to represent this as a
>minimization problem[...]

Well, yes, if you can.  Mike didn't say much about his system of
equations;  it may not be derivable from a minimization.
-- 

--Pierre Asselin, Santa Barbara, California
  pa@verano.sba.ca.us
From: dobler@sparc1.wiwi.uni-karlsruhe.de (Volker Dobler)
Newsgroups: sci.math.num-analysis
Subject: *** FACTORIZATION QUESTION ***
Date: 22 Dec 1992 09:35:40 GMT
Organization: Institut fuer Entscheidungstheorie und Unternehmensforschung Universitaet Karlsruhe (TH)
Distribution: world
Reply-To: dobler@etupc30.wiwi.uni-karlsruhe.de
NNTP-Posting-Host: etupc30.wiwi.uni-karlsruhe.de

Hi,
i'm sorry, if it is a FAQ, but i have a problem with the following
question.

I want to find two nonsingular matrices P and U with

            | U |   u
    P * N = |   |
            | 0 |   (n - u)  (this i a nul, not a big O!).

whereby N is a (n*u) Matrix (with Rank u). In the article, the author
said, i can use a PU-factorization, but i never heard of it (i'm not
a mathematical student).

So, can anybody give me a hint, an article, in which it's described or
a book (perhaps, a book or an article, which i can get in germany :->,
- the book or the article can be in english !).

Thanks for any help,
Volker
==============================================================================
|          Volker Dobler, Universitaet Karlsruhe (TH), Deutschland           |
|                                                                            |
|   e-mail: dobler@etupc30.wiwi.uni-karlsruhe.de     ,-----------------------|
|    oder     ul1f@dkauni2.bitnet                    |  I don't like chaos,  |
|  PGP20-Public Key:                                 |  but chaos likes me.  |
|        finger dobler@etupc30.wiwi.uni-karlsruhe.de |                       |
==============================================================================
From: hauser@statrix2.wu-wien.ac.at (Michi Hauser)
Newsgroups: sci.math.num-analysis
Subject: Q: ad Toeplitz matrices
Date: 30 Dec 1992 19:13:48 GMT
Organization: University of Economics and Business Administration Vienna
Distribution: world
Reply-To: hauser@wu-wien.ac.at
NNTP-Posting-Host: statrix2.wu-wien.ac.at

Hi,

Given A a quadratic, symmetric, positive definite Toeplitz matrix.

I have questions with respect to A and inverse(A). 

1) Does there exist a Cholesky decomposition algorithm using 
   the special properties of the matrix ?
2) Is a simple routine for calculating the determinant available ?

-- 
Michael Hauser

University of Economics and Business Adminstration
Department for Applied Statistics and Data Processing
Augasse 2-6, 1090 Vienna, Austria

Tel. *43/1/31336 4759
email: hauser@wu-wien.ac.at
Newsgroups: sci.math.num-analysis
From: storch@draper.com (Joel Storch)
Subject: Re: Does this product converge ???
Keywords: Infinite products, convergence
Reply-To: storch@draper.com (Joel Storch)
Organization: Draper Lab
Date: Tue, 22 Dec 1992 16:51:48 GMT


To prove that Product(k=3,infinity, Cos(Pi/k)) converges, first rewrite it as
Product(k=3,infinity,1-2 (Sin(Pi/2k))^2). This product will converge 
(absolutely) if the infinite series Sum(k=3,infinity,(Sin(Pi/2k))^2) 
converges. The Ratio Test fails here but Raabe's test shows that the series 
converges.

One source of theorems on convergence of infinite Products is Whittaker & 
Watson, "A course in Modern Analysis"
From: makarand@gazelle.larc.nasa.gov (Makarand A. Kulkarni)
Newsgroups: sci.math.num-analysis
Subject: Re: references on integration methods
Date: 29 Dec 1992 15:02:40 GMT
Organization: NASA Langley Research Center, Hampton, VA  USA
Distribution: world
NNTP-Posting-Host: gazelle.larc.nasa.gov

Assuming that you are integrating a set
of ordinary differential equations: first of all,
your friends problem appears to be one of "stability".
he may be using a very large increment in his
solutions. If he uses small enough increments, all
the integrators ought to give the same answers, unless
there is a mistake in the coding.
Seondly, some integrators are not suitable for certain
problems. Milne's method, for instance has a 
"parasitic instability" for first order odes.
Almost all integrators in existence will cause problems
if the system of equations has one exponentially growing
solution.

A good basic reference for ODEs is
Gerald and Wheatley: Applied Numerical Analysis.
(I dont know the publisher and location).

A slightly more advanced text is
Lambert J.D (1973) "Computational Methods in
Ordinary Differential Equations", Wiley, London
and New York.

Lambert has recently published a book on
Computational Methods for Systems of Equations.
(1991). I do not know the publisher and location.


As regards the truncation errors associated with various
methods, here is a brief overview.


Explicit Methods

1) Forward Euler   : First order accurate
2) Runge-Kutta     : First - Sixth order accurate
                     (depends on which particular RK is used)
3)Adams-Moulton    : Fourth order accurate


Implicit Methods  
1) Backward Euker  : First order accurate
2) Crank-Nicolson  : Second order accurate

Hope that helps.

Cheers

Makarand
Newsgroups: sci.math.num-analysis
From: Dave Dodson <dodson@convex.COM>
Subject: Re: Does this product converge ???
Originator: dodson@bach.convex.com
Date: Tue, 22 Dec 1992 19:25:35 GMT
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
Keywords: Infinite products, convergence
X-Disclaimer: This message was written by a user at CONVEX Computer
              Corp. The opinions expressed are those of the user and
              not necessarily those of CONVEX.

In article <1992Dec22.165148.20421@draper.com> storch@draper.com (Joel Storch) writes:
>
>To prove that Product(k=3,infinity, Cos(Pi/k)) converges, first rewrite it as
>Product(k=3,infinity,1-2 (Sin(Pi/2k))^2). This product will converge 
>(absolutely) if the infinite series Sum(k=3,infinity,(Sin(Pi/2k))^2) 
>converges. The Ratio Test fails here but Raabe's test shows that the series 
>converges.
>
>One source of theorems on convergence of infinite Products is Whittaker & 
>Watson, "A course in Modern Analysis"

Even simpler: The sequence of partial products is non-negative and monotone-
decreasing. Therefore it has a greatest lower bound, which must be the limit.

----------------------------------------------------------------------

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234
From: perry@vu-vlsi.ee.vill.edu (Rick Perry)
Newsgroups: sci.math.num-analysis
Subject: Re: SVD implementation
Date: 24 Dec 92 21:11:39 GMT
Organization: Villanova University

In article <1992Dec24.110843.29860@cv.ruu.nl> ger@cv.ruu.nl (Ger Timmens) writes:
>I want the singular value decomposition of a 3x3 matrix.
>I currently use the algorithm of numerical recipes.
>However I think a much simpler algorithm should be out there.

There's a method using orthogonalization by plane rotations from
the book by J. C. Nash, "Compact Numerical Methods for Computers:
Linear Algebra and Function Minimisation," Wiley 1979.  If you use
it to orthogonalize the columns, you only get a basis for the
column space, not its orthogonal complement, though you get the
complete row-space and null-space.  I am pretty sure it
is not as efficient as the standard SVD algorithm in Linpack,
but it is very simple to program.

I used Nash's technique in an application involving an N-by-3 coefficient
matrix for linear predictive coding.  By some simple preprocessing
to remove the constant LPC coefficient, the matrix was transformed to
N-by-2.  With just two columns, only one plane rotation is needed to
get the SVD, and you can even explicitly compute the singular values
without performing the whole SVD.  But I think that in general,
an N-by-3 matrix has no such simple solution.

I've implemented Nash's algorithm in Fortran, Pascal, and C, and
can mail you code if you want it.

...Rick			perry@vu-vlsi.ee.vill.edu

Dr. Rick Perry, Department of Electrical and Computer Engineering
Villanova University, Villanova, PA 19085, 215-645-4969, hm: 215-259-8734
Newsgroups: sci.math.num-analysis
From: hmiller@osiris.cso.uiuc.edu (Harry Miller)
Subject: Natural Convection and FEM
Organization: University of Illinois at Urbana
Date: Tue, 22 Dec 1992 03:50:41 GMT
Keywords: Natural Convection, FEM

I'm looking for any refernces, tips, examples, etc. of 
natural convective heat transfer using FEM.

I'm doing work on a FEM program to calculate velocity and
temperature profiles along the boundary layer of a flow along
the length of a heated cylinder.

I'm not sure how to treat the continuity equation.  Usually in
fluid flow (convective) problems FEM methods treat the continuity
equation as a parameter and use either Lagrange (sp?) multipliers
or penalty parameters.  Since these both use the gradient of the
pressure, these methods are not useable in natural convection.
I do not want to use stream functions if I do not have to.

Also, I've never done a FEM program in cylindrical coordinates.
Any help or references would be appreciated.

Thanks in advance

Harry E. Miller ----------------- just a jerk lurking on the net
hmiller@osiris.cso.uiuc.edu ----- where to send the hate mail
From: pa@curly.appmag.com (Pierre Asselin)
Newsgroups: sci.math.num-analysis
Subject: Re: Having trouble with FEM functional
Date: 28 Dec 92 20:47:53 GMT
Organization: Applied Magnetics, Goleta, CA

In <1992Dec26.221924.1@woods.ulowell.edu> chakravaa@woods.ulowell.edu writes:

>Good day,
>   I'm interested in solving a Diffusion equation problem using FEM.
>[...]
>I was having extreme difficulties in determining my course of action,
>particularly in solving for adjoint operators in the equation.

The equation is not self-adjoint.  One way to proceed it is to
discretize only the space part of the problem with finite elements.
This leaves you with a system of coupled ordinary differential
equations in time, wich you solve with finite differences.  If you want
unconditional stability for all time step sizes, you will need an
implicit scheme.  See Strang and Fix, chapter 7.
-- 

--Pierre Asselin, Magnetoresistive Head Engineering, Applied Magnetics.
  pa@appmag.com        the usual disclaimers apply.
Newsgroups: sci.math.num-analysis
From: cassorla@oak.math.ucla.edu (Mark Cassorla)
Subject: Nonpositive curvature exercise
Organization: UCLA Mathematics Department
Date: Wed, 30 Dec 92 23:29:00 GMT

The following exercise appears in "Manifolds of Nonpositive Curvature".
Any hints or solutions would be appreciated.  (Note: This is the
first exercise in the book so I think it is easily solved, but my 
head must be screwed in incorrectly.)

Let S be a surface of genus>=2 and let V=SxS.  If D is the diagonal
in V and W is a 4-manifold that admits a local diffeo over V-D that
is ramified at D, show that W admits no smooth metric of nonpositive
curvature.

Newsgroups: sci.math.num-analysis,alt.sources.wanted
From: broussea@DMI.USherb.CA (Normand Brousseau)
Subject: Re: C-code for Simplex algorithm wanted
Organization: Universite de Sherbrooke -- Dept. d'Informatique
Date: Tue, 22 Dec 1992 17:48:55 GMT

Hi

I'm very interest to a c-code of simplex.
Please send me a copy if possible (or adress to find it).

Thanks

Normand Brousseau
Graduate student (Ph.D.)

-- 
Normand Brousseau (Maths) 
normand.broussea@dmi.usherb.ca
DMI, Universite de Sherbrooke, 2500 boul. Universite
Sherbrooke, Quebec, Canada, J1K 2R1
Newsgroups: sci.math.num-analysis
From: ger@cv.ruu.nl (Ger Timmens)
Subject: SVD implementation
Date: Thu, 24 Dec 1992 11:08:43 GMT
Organization: University of Utrecht, 3D Computer Vision Research Group

I want the singular value decomposition of a 3x3 matrix.
I currently use the algorithm of numerical recipes.
However I think a much simpler algorithm should be out there.

Any pointers ?

Thanks in advance,
-- 
|I|        Ger Timmens         |I| If you're not part of the solution, |I|
|M|  3D Computer Vision Group  |M| you're part of the problem!         |M|
|H|    e-mail ger@cv.ruu.nl    |H+-------------------------------------+H|
|O|   or  timmens@cs.unc.edu   |O| Album by Joe Henderson (best tenor) |O|
Newsgroups: sci.math.num-analysis
From: broussea@DMI.USherb.CA (Normand Brousseau)
Subject: Pascal code source for mixed integer programs wanted.
Organization: Universite de Sherbrooke -- Dept. d'Informatique
Date: Wed, 23 Dec 1992 20:18:14 GMT

Hi

I need a pascal source code for the following mixed integer program:

                       Max cx
                      s.t.   
                       Ax + Dy = b
                        x >= 0
                        y = 0 or 1

Thanks for any informations.
-- 
Normand Brousseau, graduate student Ph.D. Maths 
normand.brousseau@dmi.usherb.ca
DMI, Universite de Sherbrooke, 2500 boul. Universite
Sherbrooke, Quebec, Canada, J1K 2R1
From: phys2108@waikato.ac.nz
Newsgroups: sci.math.num-analysis
Subject: Yet another question on FE methods
Date: 22 Dec 92 14:40:56 +1300
Organization: University of Waikato, Hamilton, New Zealand

Hi,
	I've just got the book Finite Element Analysis, by David S. Burnett.
It appears at first sight to be very good, and very thorough. Any opinions on
it?, and are there any known ftp sights for the FE code UNAFEM around.
Geoff.
P.S. Sorry if ftp sights are given in the book etc., but like I've said, I
have only just opened it up.

Newsgroups: sci.math.num-analysis
From: andy@laguna.santafe.edu (Andy Mell)
Subject: Re: Natural Convection and FEM
Date: Wed, 23 Dec 92 03:14:18 GMT
Organization: Santa Fe Institute
Keywords: Natural Convection, FEM

In article <Bzn6oH.1HE@news.cso.uiuc.edu> hmiller@osiris.cso.uiuc.edu (Harry Miller) writes:
>I'm looking for any refernces, tips, examples, etc. of 
>natural convective heat transfer using FEM.
>
>I'm doing work on a FEM program to calculate velocity and
>temperature profiles along the boundary layer of a flow along
>the length of a heated cylinder.

Dont bother with FEM, its overcomplicated for problems such as this. I suggest
you take a look at this paper, which deals with exactly what you want.

Pulko, Green, Johns - TLM and thermal diffusion, Int.J.Num.Meth.Eng, vol.24
pp1333-1341, 1987

A
-- 
-------------------------------------------------------------------------------
Andy Mell, Applied Physics Department,  |   andy@santafe.edu
University of Hull, Hull, HU7 6RX       |   amell@nyx.cs.du.edu
England.                                |   torq@gnu.ai.mit.edu
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.math.num-analysis
Subject: Re: basins of attraction
Summary: Here's a simple example...
Keywords: iteration basin attraction algorithm
Date: 28 Dec 92 17:23:38 GMT
Article-I.D.: pith.1hnd6qINN4h8
Distribution: inet
Organization: University of Oregon Campus Information Exchange
NNTP-Posting-Host: cie.uoregon.edu

In article <erwin.725499996@trwacs> erwin@trwacs.fp.trw.com (Harry Erwin) writes:
>The basin of attraction for an attractive fixed point is the region that
>converges on the point under the operation of the function. Look at the
>inverse of the function. The region that nearby points reach under the
>operation of the inverse is the basin you're looking for.

Conceptually maybe, but is this practical?  Consider the following example:

The map  F(x) = x - tan(x)  has a third order attracting fixed point
at  x = pi .  The immediate basin is, I believe, bounded by a repelling
2-cycle.  How do I get a handle on this basin numerically?

>Note that if the
>function operates discretely, the resulting "basin" may well be quite
>strange...

I'd be happy with the _immediate_ basin (which is an open interval).

-- 
Tom Scavo
scavo@cie.uoregon.edu
From: hcobb@fly2.berkeley.edu (Henry J. Cobb)
Newsgroups: sci.math.num-analysis
Subject: LU decomposition on very large matrix.
Date: 23 Dec 92 14:38:56
Organization: /rubin/hcobb/.organization
Distribution: inet
NNTP-Posting-Host: fly2.berkeley.edu


I am interested in C code for the manipulation of a VERY large matrix.
Basically, what I need to do is perform an LU decomposition on a matrix
too large to operate on the whole thing at once.  Therefore, I need an
algorithm that allows me to operate on chunks of the matrix at a time,
and which allows an in-place LU decomposition, so that I can minimize
the amount of disk storage necessary for the computations.  Any
help is GREATLY appreciated.
--
	Henry J. Cobb	hcobb@fly2.berkeley.edu	SFB Tyrant
	"Once it becomes possible to do something, it gets very difficult to
undo it.  Whether its automobiles, computers or nuclear weapons, invention has
always been the mother of necessity."
Newsgroups: sci.math.num-analysis
From: a722756@roper.mc.ti.com (W. Donald Rolph)
Subject: Re: LU decomposition on very large matrix.
Originator: a722756@roper.mc.ti.com
Organization: Texas Instruments / Attleboro Mass / USA
Distribution: inet
Date: Mon, 28 Dec 1992 13:26:20 GMT


You should also look at the optsol articles in the INternational Journal of
Numerical  Methods in Engineering (aspprox 1984), and Irons article on wave front
solvers IJNME about 1983.
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263
From: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Newsgroups: sci.math.num-analysis
Subject: Re: Natural Convection and FEM
Date: 27 Dec 92 21:24:56 GMT
Reply-To: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Organization: Delft University of Technology
Originator: rcpshdb@dutrun2.tudelft.nl

In article <a1grvn-@SantaFe.edu> Andy Mell writes:
> Dont bother with FEM, its overcomplicated for problems such as this.

Still very true. Alas ...

In article <1992Dec23.094321@roper.mc.ti.com> W. Donald Rolph writes:
> I always get amused by comments such as this.

Well, *I* get always amused (not really) by stubborn comments such as THIS:

> FEA is merely the establishment of a set of trial functions which are valid
> over a specific region in the domain (rather than the total domain),
> and which are typically constructed in such a way that the valid domain need
> not be rectilinear. As such, virtually every numerical method is a subset
> of FEA (I admit to some issues with Boundary Element Methods).

Gee, I thought I had posted in this newsgroup every possible counter-argument
& even created an "anonymous ftp" site (with SUNA articles), each one of these
aiming to _prove_ that the above statement is definitely incorrect. Instead, it
is a prejudice of the severest kind. It will get us nowhere. And it does really
big harm to the science of numerical methods as a whole. Because it will widen
the gulf between FEA and FV methods.
-- 
* Han de Bruijn; Applications&Graphics | "A little bit of Physics * No
* TUD Computing Centre; P.O. Box 354   | would be NO idleness in  * Oil
* 2600 AJ  Delft; The Netherlands.     | Mathematics" (HdB).      * for
* E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood
Newsgroups: sci.math.num-analysis
From: rairan@ecf.toronto.edu (RAI Ranjan)
Subject: Papers from Netlib
Organization: University of Toronto, Engineering Computing Facility
Date: Tue, 29 Dec 1992 04:09:27 GMT

Are the papers listed in the Netlib bibliography available on-line 
somewhere?  If so, could someone tell me how I can access them?

In particular, I am looking for the following paper:

author = M. Akguel 
title = "On the exact solution of a system of linear homogeneous
       equations via a projective algorithm"
journal = "Arabian Journal for Science and Engineering"
volume = 15
number = 4
year = 1990

Many Thanks.
 
-- 
Ranjan Rai                             <rairan@ecf.toronto.edu> 
Engineering Science 9T3                <rr@odin.control.toronto.edu> 
University of Toronto                    
Newsgroups: sci.math.num-analysis
From: monagan@inf.ethz.ch (Michael)
Subject: Re: SVD implementation
Summary: symbolic approach
Organization: Dept. Informatik, Swiss Federal Institute of Technology (ETH), Zurich, CH
Date: Mon, 28 Dec 1992 19:56:02 GMT

In article <63058@mimsy.umd.edu>, stewart@cs.umd.edu (G. W. Stewart) writes:
> In article <1992Dec24.110843.29860@cv.ruu.nl> ger@cv.ruu.nl (Ger Timmens) writes:
> #I want the singular value decomposition of a 3x3 matrix.
> #I currently use the algorithm of numerical recipes.
> #However I think a much simpler algorithm should be out there.
> #
> #Any pointers ?
> 
> You've run into a situation that frustrates a lot of people.  In
> principle, it should be possible to solve eigenvalue (or singular
> value) problems of order 2, 3, and 4 directly using the formulas for
> solving quadratic, cubic, and quartic equations.  In practice, though,
> the complexity of the formulas makes the effort practical only for 2x2
> problems.  And even then the difficulties are great.  When Charlie Van
> Loan (of Golub and Van Loan fame) was a graduate student he produced a
> forty page manuscript entitled "An Algorithm for the Generalized
> Matrix Eigenvalue Problem {$Ax=\lambda Bx$} for the Important Case
> {$N=2$}", and it was none too short.  You will probably do well to
> stick with general code.
> 
> Not that I recommend the Numerical Recipes code.  I've been told that
> it is a modification of the LINPACK code, the modifications causing
> it to fail in some cases.  I would stick with the LINPACK or LAPACK
> code which is available on netlib.
> 
> Pete Stewart
> 
===========
I agree 100% with what Pete Stewart says in general.
The fact that "the important case n=2" is doable is largely? because
the roots of the characteristic polynomial are always simple,
simple in the sense that they are small and easily computed.
However, for the case in question n=3, you could try to factor the
characteristic polynomial symbolically.  If your 3 by 3 matrix
has a special form, you might get lucky.  The formulae for
the singular values will be relatively simple if it factors.
If the characteristic polynomial does not factor, as Pete Stewart
incidates, the formulae will too complicated.
One last possibility to try (I have never tried to do this
for computing a svd, I've only tried it for computing eigenvectors,
but the priciple should work) is to let a variable alpha denote
the root of the characteristic polynomial.  Compute the svd
symbolically in terms of this symbol alpha.  Later, it 
will take on the 3 numerical values -- roots of the characteristic polynomial.

Michael Monagan
From: paulm@hpcvra.cv.hp.com (Paul McClellan)
Date: Wed, 23 Dec 1992 17:14:59 GMT
Subject: Re: question about a reference
Organization: Hewlett-Packard Co., Corvallis, OR, USA
Newsgroups: sci.math.num-analysis

> 
> I found a reference that might interest me, but the people in the library
> where I work can't find it.
> Does anybody have more information about :
> 
> P. Kaps, G. Wanner : Rosenbrock-type methods of high order. In press (1979)     ?
> 

Try:

Kaps, P., and Wanner, G.  A study of Rosenbrock-type methods of high order.
Institut fur Mathematik and Geometrie, Universitat Unnsbruck, Innsbruck,
Austria, 1979.

Newsgroups: sci.math.num-analysis