HDTenEightyP/NetNews huggingface dataset:
From: sshankar@td2cad.intel.com (Sadasivan Shankar)
Newsgroups: sci.math.num-analysis
Subject: Re: Advantages/Disadvantages of Galerkin Method
Date: 11 Jan 93 19:26:25 GMT
Reply-To: sshankar@td2cad.intel.com (Sadasivan Shankar)
Organization: Intel Corporation, Santa Clara, CA USA


Some general references for Galerkin techniques

	Computational Galerkin Methods by C.A.J. Fletcher

	Numerical Methods in Partial Differential Equations by L.Lapidus and Pinder

	Finite Element Method  G. Strang and Fix

	Non-linear Methods ..... B. Finlayson

There are other authors like Zeinkinowicz (sp ?), Hughes, and so on.  The book by
Strang  and the one by Finlayson are well worth looking into, for good background and a
wider perspective.

S.Shankar
Tech CAD
INTEL
Newsgroups: sci.math.num-analysis
From: simardr@IRO.UMontreal.CA (Richard Simard)
Subject: Re: Calculating norm of a function
Reply-To: simardr@IRO.UMontreal.CA (Richard Simard)
Organization: Universite de Montreal
Distribution: usa
Date: Tue, 5 Jan 1993 18:58:20 GMT

In article <!672sl_@rpi.edu> sassoj@rs6412.ecs.rpi.edu (John J. Sasso Jr.) writes:
>
>   Given a function f in L^2(R), which exists on the interval [a,b], how
>would I go about calculating its L^2-norm?  Does there exist a numerical
>algorithm which can do this?
>
the simplest choice of norm would be:

integral(from a to b) dx f*(x) f(x)
where f* is the complex conjugate

- if f is real then 
integral(from a to b) dx f(x)^2

other choices of norms are possible depending on your problem;
for ex.

integral(from a to b) dx f(x)^2/[(x-a)(b-x)]^t

where t is a real such that the integral exists.

--
From:  simardr@iro.umontreal.ca
From: stewart@cs.umd.edu (G. W. Stewart)
Newsgroups: sci.math.num-analysis
Subject: Re: Condition Number
Date: 12 Jan 93 06:25:25 GMT
Organization: U of Maryland, Dept. of Computer Science, Coll. Pk., MD 20742

In article <1993Jan11.083253.9521@dutrun2.tudelft.nl> rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
>The condition number of a matrix  A  is defined as the absolute value of
>its largest eigenvalue divided by its smallest eigenvalue. Right?
>
>I'm at loss how this is related to the loss of decimals when solving the
>equations system:
>                      A.x = b
>
>Can someone out there provide a simple argument?

David Dodson has provided a nice derivation of the relevant
perturbation theory.  However, some additional comments are needed to
get to loss of decimals.  (I'll use LaTeX notation here, with
apologies to those who don't read it.)

If we replace $A$ by $A+E$, we find that the change $h$ in the
solution satisfies (up to second order terms in $E$)
\[
\|h\|/\|X\| \leq \kappa(A)\|E\|/\|A\|,
\]
where
\[
\kappa(A) = \|A\| \|A^{-1}\|
\]
is the condition number of $A$.  Now if $\|E\|/\|A\| = 10^{-t}$, then
the elements of $A$ will be perturbed in their $t$th decimal digits
(some qualifications about balance in the sizes of the elements of $E$
and $A$ are needed here).  Hence if $\kappa(A) = 10^{k}$, then
$\|h\|/\|X\| \leq 10^{k-t}$, so that the components of $x$ are
perturbed in their $(t-k)$th digits.  In ordinary English, if $A$ is
known to $t$ digits and $\kappa(A) = 10^{k}$, then $x$ will be known
to $t-k$ digits.

In particular, if a stable algorithm like Gaussian elimination is used
to solve the system, then $t$ is the number of digits used in the
computation.  Thus, if you try to solve a system with condition
number $10^{k}$ using Gaussian elimination, you can expect a loss
of about $k$ digits in the solution.

All this is a useful oversimplification.  For the complete story, see
an introductory text on matrix computations.

Pete Stewart
From: sshankar@td2cad.intel.com (Sadasivan Shankar)
Newsgroups: sci.math.num-analysis
Subject: Re: Advantages/Disadvantages of Galerkin Method
Date: 8 Jan 93 19:04:57 GMT
Reply-To: sshankar@td2cad.intel.com (Sadasivan Shankar)
Organization: Intel Corporation, Santa Clara, CA USA


Galerkin methods with finite elements are very widely used for parabolic systems like
Navire-Stokes. The conventional Galerkin Finite Elements (GFEM) are as estable for these
systems.  However, for predominantly hyperbolic systems (Euler Equations, Vlasov Equations),
GFEM loses its stability.  As a result, some form of stabilization is necessary like
a streamline upwinding has to be added.  There are also other ways to stabilize the GFEM
for hyperbolic systemsby using the so-called Petrov-Glaerkin techniques in which you
have the rial functions different from the test functions.  SOme error estimates are
available for different methods (Claes Johnson (1986), T.J. Hughes (1982)) and so on.

	Now for non-linear systems; It is well known that Navier-Stokes equations can
be primary source of chaos under appropriate parameter conditions (the Lorenz equations).
It is possible to use GFEM for such systems as well. However, it should be noted that
chaotic behavior is a characteristic of the "system of equations that one is solving" and
will manifest independent of the numerical technique.  Appropriate manipulation of the
same technique (GFEM for instanace) should not be a problem to study this behavior.

	It has also been observed that systems of equations can change their behavior
inside the domain.  FOr example parabolic systems can be come hyperbolic (boundary layer
flow, non-newtonian polymeric fluids).  In cases like these, GFEM (assuming that stabilizing
properties are already incoporated) can be used.  
	Hope that the above lines answer at least some of your questions.

S.Shankar
Tech CAD
INTEL Corporation
Newsgroups: sci.math.num-analysis
From: mckenney@cims.nyu.edu (Alan McKenney)
Subject: Re: Condition Number
Followup-To: sci.math.num-analysis
Summary: condition number is not related to eigenvalues
Originator: mckenney@gauss.cims.nyu.edu
Keywords: eigenvalues, singular values, condition number
Organization: Courant Institute, NYU, NY, NY, USA
Date: Tue, 12 Jan 1993 16:09:32 GMT


In article <1993Jan11.214251.12368@news.eng.convex.com>
dodson@convex.COM (Dave Dodson) writes:
>In article <1993Jan11.083253.9521@dutrun2.tudelft.nl>
>rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
>>The condition number of a matrix  A  is defined as the absolute value of
>>its largest eigenvalue divided by its smallest eigenvalue. Right?
>>
>>I'm at loss how this is related to the loss of decimals when solving the
>>equations system:
>>                      A.x = b
>>
>>Can someone out there provide a simple argument?

  [Dave Dodson's good explaination deleted]

One thing that no one has remarked on: The original poster's reference
to *eigenvalues*.

    As Dave Dodson points out, the condition number of A is
norm(A) * norm(A-inverse).  No mention of eigenvalues.

    In fact, the condition number of a matrix has (almost) nothing to
do with the eigenvalues, as the example

        ( 1  t )                        -1   ( 1  -t )
    A = (      )   for t >> 1 shows:   A   = (       )
        ( 0  1 )                             ( 0   1 )

so the eigenvalues are both 1, but norm(A) = norm(A-inverse)
which are approximately  t, so the condition number is approx.
t**2.

    What the condition number *is* related to are the *singular values*.
For more info, look in a good book on numerical linear algebra
(e.g., Golub & van Loan's _Matrix_Computations_) on the "singular
value decomposition" (or SVD).  The SVD, once understood, makes
a lot of this a whole lot simpler to understand.


-- 
Alan McKenney        E-mail:  mckenney@cims.nyu.edu         (INTERNET)
Courant Institute,NYU,USA     ...!cmcl2!cims.nyu.edu!mckenney   (UUCP)
From: mapmh@gdr.bath.ac.uk (M Hagger)
Newsgroups: sci.math.num-analysis
Subject: Re: Eigenvectors of the sum of two symmetric matrices
Date: 8 Jan 93 15:31:50 GMT
Organization: School of Mathematics, University of Bath, UK

In the referenced article, mmt@ccu1.aukuni.ac.nz (Mark Thomson) writes:
>If and A and B are two symmetric matrices, can anyone tell me whether it
>is possible to relate the eigenvectors of (A+B) and their corresponding
>eigenvalues to the eigenvectors and eigenvalues of A and B.

If I remember correctly there are bounds available for the changes in the
eigenvalues, for general A and B.  In general I don't think it is possible 
to give exact new eigenvalues.

You could try any of the following for more details:

J.H Wilkinson - The algebraic eigenvalue problem (1965)
Golub and Van Loan - Matrix Computations, 2nd edition (1989)

Hope this is of some help.

Mark
From: makarand@gazelle.larc.nasa.gov (Makarand A. Kulkarni)
Newsgroups: sci.math.num-analysis
Subject: Re: NAG routine D02BAF uses runge-kutta-MERSON ??
Date: 4 Jan 1993 19:54:49 GMT
Organization: NASA Langley Research Center, Hampton, VA  USA
Distribution: world
NNTP-Posting-Host: gazelle.larc.nasa.gov
Keywords: Merson, nonlinear problems




In article <1993Jan4.141352.5937@fys.ruu.nl>, walsteyn@fys.ruu.nl (Fred Walsteijn) writes:
|> I have just read that the NAG routine D02BAF is based on
|> a Runge-Kutta-Merson embedded formula.
|> Is it the same formula as mentioned in the books of
|> Lambert (1991) and Butcher (1987) ?
|> 
|> If it is, does that mean that its error truncation estimate
|> is ``easily defeated'' (cite, as I remember it from one of
|> the abovementioned books) ?
|> The reason is that the ``high order'' component has a high
|> (fifth) order of accuracy only for linear problems.
|> It cannot have fifth order of accuracy for all (e.g. nonlinear) problems
|> as it has only five stages (Butcher, 1987).
|> 
|> Thanks for any clarifying remarks...
|> -----------------------------------------------------------------------------
|> Fred Walsteijn                                | Internet: walsteyn@fys.ruu.nl
|> Institute for Marine and Atmospheric Research | FAX:      31-30-543163
|> Utrecht University, The Netherlands           | Phone:    31-30-533169


Most error estimates for integrators are based on what is called
the "linear test equation". It is extremely difficult if not
impossible to obtain local truncation error estimates for 
nonlinear problems. Normally error estimates for nonlinear
problems are obtained by linearizing the equation(s).

As a general rule, there will be a loss of stability and
accuracy when integrators are used for nonlinear equation(s).
This is true of the Runge-Kutta Merson also.  Conversely
a higher order accurate method for a linear problem will be
accurate for a nonlinear problem.

From an implementation point of view, the Runge-Kutta 
family of integrators are robust, accurate and stable. I
have worked with the four stage Runge-Kutta, the Runge-Kutta
Merson and the six stage Runge-Kutta Fehlberg and have found
them to quite reliable. Again, if there are exponentially 
growing terms, then an error analysis breaks down. 

If someone out there has any references on non-linear
stability theory and error estimates for non-linear 
problems, please post them.

Hope this helps somewhat.

Regards


Makarand
makarand@puma.larc.nasa.gov
Newsgroups: sci.math.num-analysis
From: wskelly@laurel.ocs.mq.edu.au (William Skelly)
Subject:  Numerical Recipes
Keywords: Press et al.
Organization: Macquarie University, Australia.
Date: Tue, 12 Jan 1993 20:44:30 GMT

Hi People,

Does anyone know whether the authors of numerical recipes
(Press, Flannery, Teukolsky and Vetterling) allow their
routines to be used in public domain software?  I own a
copy of their book and have used two routines that are
quite beyond what I could program (at least in this life
time!) and I would like to share the software that I have
used these routine in.  Up to now I have stripped the two
routines and noted that you need to supply such and such,
but I thought I'd ask...

Perhaps one of the authors is on the net?

Cheers,
Chris
 


Newsgroups: sci.math.num-analysis
From: barry@arnold.math.ucla.edu (Barry Merriman)
Subject: Re: Octave -- a high-level language for numerical computations
Organization: UCLA, Mathematics Department
Date: Tue, 12 Jan 93 02:39:57 GMT

In article <1iskmhINNokt@geraldo.cc.utexas.edu> jwe@che.utexas.edu (John W.  
Eaton) writes:
> ------------------------------
> ANNOUNCING:  Octave ALPHA test
> ------------------------------
> 
> What is Octave?
> ---------------
> 
> 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.

What would be the advantage (besides $) of Octave over 
Maple/Mathematica/MATLAB ?

Isn't it YANKEE (Yet Another Numerical Komputing EEnvironment)?


--
Barry Merriman
UCLA Dept. of Math
UCLA Inst. for Fusion and Plasma Research
barry@math.ucla.edu (Internet; NeXTMail is welcome)


Newsgroups: sci.math.num-analysis
From: robin@fractal.ireq-num (Robin Duquette )
Subject: MINOS
Reply-To: robin@fractal.ireq-num
Organization: Sun Microsystems, Inc.
Date: Mon, 4 Jan 1993 20:21:08 GMT

---

I would appreciate very much if somebody could give me the E-mail
address of Michael Saunders or Bruce Murtagh (the authors of MINOS).

Thanks in advance.

--------------------------------------------------------------------------------
Robin Duquette                              E-mail: robin@ireq-num.hydro.qc.ca
Service Methodes numeriques                 phone : (514) 652-8239
Institut de recherche d'Hydro-Quebec        fax   : (514) 652-8005
1800 montee Ste-Julie,
Varennes (Quebec) Canada J3X 1S1
--------------------------------------------------------------------------------

Newsgroups: sci.math.num-analysis,comp.sys.super,comp.parallel
From: domik@wilkinson.cs.colorado.edu (Gitta Domik)
Subject: High-Performance Scientific Computing -- for Undergraduates
Organization: University of Colorado, Boulder
Date: Wed, 6 Jan 1993 20:54:39 GMT


		Summer Workshop for Undergraduates
	      High-Performance Scientific Computing 
	University of Colorado, May 24 - June 4, 1993


This residential workshop is designed for upper division undergraduate 
students who are interested in learning about the use of supercomputers,
high-performance workstations, and  visualization in scientific 
computing. Workshop participants will use a Connection Machine (CM-2), 
a Cray Y-MP, DEC 5000 and SGI Indigo workstations, AVS and IDL (scientific
visualization tools) for solving problems in molecular dynamics, 
wave motion, and visualization of data.

Participants will reside in Kittredge Residence Halls on the University campus.
Classes and laboratory sessions will be held in the Engineering Center
located nearby. Residence expenses (room and board) will be paid by
a grant from the National Science Foundation. Transportation expenses will
not be covered.

Attendance at the workshop will be limited to sixteen students. Selection
of participants will be based on the following criteria:

	Statement of interest. This statement describes
	why the applicant is interested in participating in the workshop, 
	relevant academic experience and interests, and long-range goals.

	Letter of recommendation by faculty member. This letter should be 
	written by a faculty member who has served as the student's
	academic advisor or teacher. It should describe the student's 
	strengths, academic performance, and potential for achievement.

	Satisfying the prerequisites. The prerequisites are experience with
	the Unix operating system, two semesters of calculus, one semester of
	numerical analysis, two semesters of courses in physical or biological
	science.

Some course materials are available by anonymous FTP from cs.colorado.edu
in directory /pub/cs/HPSC.

Inquiries and applications should be sent to: Professor Elizabeth Jessup,
Dept. of Computer Science, University of Colorado, Boulder, CO 80309-0430;
tel. (303) 492-0211; e-mail jessup@cs.colorado.edu. 

		APPLICATION DEADLINE MARCH 31

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

There is no application form, but your application letter should include 
the following:

=      Name
=      Affiliation and position or class
=      Mailing address
=      Phone number
=      Email address
=
=      Statement of interest as described in the announcement.
=      A description of your relevant background including your experience
=         with the prerequisites listed in the announcement.
=      The letter of recommendation from a faculty member.
From: ratier@velvet.laas.fr (Nicolas Ratier)
Newsgroups: sci.math.num-analysis
Subject: Karman equations
Date: 21 Dec 92 16:49:33 GMT
Organization: LAAS-Centre National de la Recherche Scientifique Toulouse, France
Originator: ratier@velvet

Hi,

         I have to solve the Karman's system of equation :
-------------------------------------------------------------------
  (Wxxxx + 2 Wxxyy + Wyyyy) - (Fyy Wxx + Fxx Wyy - 2 Fxy Wxy) = P
  (Fxxxx + 2 Fxxyy + Fyyyy) + (Wxx Wyy - Wxy Wxy)       = 0
------------------------------------------------------------------- 

    on a rectangulare domaine, the plate is clamped.

so the limites conditions for W (the deflection) are dW/dn = 0
                                                      W    = 0

   but what are the limites conditions for the fonction F ????????
I didn't find anything on it.

	Does anybody had work on this problem ?
        please email me at :   ratier@laas.laas.fr
        Thanks

                           Nicolas 


-- 

   -------------------------------------
   |       L.A.A.S.   (France)         |
   |                                   |
Newsgroups: sci.math.num-analysis
From: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Subject: Re: Advantages/Disadvantages of Galerkin Method
Originator: rcpshdb@dutrun2.tudelft.nl
Reply-To: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Organization: Delft University of Technology
Date: Mon, 11 Jan 1993 08:11:04 GMT

In article <1993Jan8.083828@roper.mc.ti.com> W. Donald Rolph:
>      - a pure Galerkin forumlation typically requires trial functions of twiceUnread news in news.config                                 1 article  +  412 oldUnread news in news.config                                 1 article  +  412 old
>             the order of an equivalent Variational formulation

"forumlation" etc. ... Whoa! Your articles repeadtedly turn out to be a mess!

How about correct syntax, 80 columns ASCII, and the like?

Wouldn't you care a bit more about your readers public, Don?
-- 
* 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
From: ajt@resmel.bhp.com.au (Andrew Telford)
Newsgroups: sci.math.num-analysis
Subject: Re: Octave -- a high-level language for numerical computations
Date: 12 Jan 93 07:14:37 GMT
Organization: BHP Research - Melbourne Laboratories
Distribution: world
NNTP-Posting-Host: peregrin.resmel.bhp.com.au
In-reply-to: jwe@che.utexas.edu's message of 11 Jan 1993 20:18:25 GMT


Are there any significant differences between Octave
and the MATLAB clone RLab which is also under the GPL and
in alpha test:

mizar.docs.uu.se /pub/alpha/RLaB/rlab-0.30.tar.Z

Andrew 
--
     /\/\       Process Control Group 
    / / /\      BHP Research - Melbourne Laboratories
   / / /  \     245 Wellington Rd, Mulgrave, 3170
  / / / /\ \    AUSTRALIA
  \ \/ / / /
   \  / / /              Phone   :  +61-3-560-7066
    \/\/\/      AARnet/Internet  :  ajt@resmel.bhp.com.au
From: pkbhatti@kopth004.delcoelect.com (Pardeep K. Bhatti)
Newsgroups: sci.math.num-analysis
Subject: Re: Advantages/Disadvantages of Galerkin Method
Date: 8 Jan 93 13:42:57 GMT
Organization: Delco Electronics Corp.

In article <yg!31aq@rpi.edu> sassoj@aix.rpi.edu (John J. Sasso Jr.) writes:
>
>    The Galerkin method, which is used to approximate solutions to differential
>   equations, appears to be a pretty interesting technique.  However, I am 
>   not too knowledgable about it, so I'd like to know what is its advantages
>   and disadvantages.  Also, how does it fair against nonlinear ODEs and PDEs,
>   which tend to have chaotic solutions.  If anyone has any good introductory
>   references to the Galerkin method, I would like to know about them.
>
>                          -- John

Galerkin method is a particular type of weighted residual technique in
which the shape (trial) functions themselves are used as weighting
functions. There are several different types of weighted residual methods
such as point collocation, subdomain collocation, least squares, and
Galerkin. These are all powerful techniques, and are very simple to
implement in finite element analysis because you don't have to find a
variational formulation for nonstructural problems. Galerkin method is the
most popular weighted residual method in finite element analysis, and it
can be proved that if the problem has a classical variational form,
Galerkin method will give the exact same results as a variational technique
such as Rayleigh-Ritz.

Look in "The Finite Element Method" by Zienkiewicz for more details about
this method.
-- 
Pardeep K. Bhatti                         pkbhatti@kopth004.delcoelect.com
Delco Electronics Corporation
GM Hughes Electronics
***  The opinions expressed are mine, not necessarily of my employer.  ***
Newsgroups: sci.math.num-analysis
From: ss4i@kelvin.seas.Virginia.EDU (Sriram  Srinivasan)
Subject: question about BALANC from EISPACK
Originator: ss4i@kelvin.seas.Virginia.EDU
Organization: University of Virginia
Date: Thu, 7 Jan 1993 23:55:43 GMT

Hi,

   I had the following question about the BALANC routine from EISPACK.

   Given a matrix A, BALANC gives the balanced matrix

          Ab = T*A*inv(T)

   and also some information in the variables LOW, IGH, and SCALE which
   determine the similarity transformation T.

   Does anybody know how to construct a T explicity, for all A?

   Thanks.                       

   Sriram (spoiled by MATLAB)

   (ss4i@kelvin.seas.virginia.edu)
Newsgroups: sci.math.num-analysis
From: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Subject: Re: Robert Skeel, you suck.
Originator: rcpshdb@dutrun2.tudelft.nl
Reply-To: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Organization: Delft University of Technology
Date: Tue, 12 Jan 1993 08:18:33 GMT

In article <93011.170832U53644@uicvm.uic.edu> Joseph B. Dunphy:
> It is a fact that there are some very good researchers who happen to be truly
> awful teachers, [ ... ]

I don't believe it.
There are some very bad teachers who happen to be truly awful researchers too.
-- 
* 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: rayes@Goat.mcs.kent.edu (Mohamed Omar Rayes)
Subject: Parallel Numerical Algorithms Text Book
Organization: Kent State University
Date: Wed, 6 Jan 1993 02:18:46 GMT

  A friend of mine who is involved in applied mathemtics problems that
require intensive computing power is looking for a good and introductry
text in parallel numerical algorithms. If you know of a text that
emphasizes pratical as opposoed to theoretical algorithms, please send
e-mail to rayes@mcs.kent.edu. Thanks in advance.