HDTenEightyP/NetNews huggingface dataset:
From: chakravaa@woods.ulowell.edu
Subject: Having trouble with FEM functional
Organization: University of Lowell
Date: Sun, 27 Dec 1992 03:19:24 GMT

Good day,
   I'm interested in solving a Diffusion equation problem using FEM.  However,
I'm having difficulty putting the equation into a functional form that can be
manipulated.  The equation is a 1-D equation with the following boundary
conditions:
       u(x,0) = f(x) = sin x
and    u(0,t) = u(L,t) = 0  as bc's.
the actual equation as such comes to a solution of
   u(x,t) = sin (x) (e**(-k**2 t )
when solved analytically.
When attempting to use the Euler-Lagrange eqn. to find the functional form,
I was having extreme difficulties in determining my course of action,
particularly in solving for adjoint operators in the equation.
Any help would be appreciated.
 
Ut = k**2 Uxx is the Diffusion equation.

Thanx.
A.C.
From: agw@ground.cs.columbia.edu (Art Werschulz)
Newsgroups: sci.math.num-analysis
Subject: Multivariate Legendre polynomials
Date: 28 Dec 1992 11:04:28 -0600
Organization: CS Dept, University of Texas at Austin
Distribution: inet
Reply-To: agw@cs.columbia.edu
NNTP-Posting-Host: cs.utexas.edu

Hi.

[If this is a repost, please blame our news posting program.  It said
that the previous post didn't take.]

Does anybody have references about multidimensional Legendre
polynomials defined over simplexes in $d$-dimensional space?  

Thanks.

      Art Werschulz
      InterNet:  agw@cs.columbia.edu
      ATTnet:    Columbia University (212) 939-7061
                 Fordham University  (212) 636-6325
Newsgroups: sci.math.num-analysis
From: erwin@trwacs.fp.trw.com (Harry Erwin)
Subject: Re: basins of attraction
Keywords: iteration basin attraction algorithm
Organization: TRW Systems Division, Fairfax VA
Date: Sun, 27 Dec 1992 23:46:36 GMT

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

Cheers,
-- 
Harry Erwin
Internet: erwin@trwacs.fp.trw.com

Newsgroups: sci.math.num-analysis
From: dtl8v@holmes.acc.Virginia.EDU (Heracleitus)
Subject: Numerical Recipes 2nd ed.?
Originator: dtl8v@holmes.acc.Virginia.EDU
Organization: University of Virginia
Date: Sun, 27 Dec 1992 02:03:27 GMT


  I have seen Numerical Recipes for Fortan in the 2nd edition, with
updated wavelet algorithms and such, but I was wondering if anyone
knows the planned publication schedule for Numerical Recipes in C or
Pascal, as there are already example books for the "2nd edition" in C
and Pascal.

Doug Lamb
dtl8v@Virginia.EDU

And what about Numerical Recipes for C++, or N.R. for Ada?? :-)
Newsgroups: sci.math.num-analysis
From: jhmiller@IASTATE.EDU (James H Miller)
Subject: Hyperbolic Systems...(question)
Reply-To: jhmiller@IASTATE.EDU (James H Miller)
Organization: Iowa State University
Date: Tue, 29 Dec 1992 20:08:47 GMT


Ok here it is......

First start with a system that is hyperbolic or at least quasi-hyperbolic.
Such as...


        [U]     +     [F]    =   [0]                         (1)
           t             x            


where [F] is (or has the property of being) homogeneous of degree one in [U]. 
This means(I think..) that the above equation can be written as :

        [U]      +     [A][U]    = 0                           (2) 
           t                 x 	
		

Where [A] is given as d[F]/d[U] = [A].    
For the above system to be purely hyperbolic the eigenvalues of [A] must all
be real and distinct. If the eigenvalues are repeated the system can be
"hyperbolic" if a set of eigenvectors are linearly independent.
Given this hyperbolic system of equations (or at least quasi-hyperbolic), I
would like to show the following:



        [R]   +  [A][R]   = 0                                  (3)
           t           x            

	

	where [R] is a square matrix whose columns consist of the right eigenvectors of
[A]. 
This type of equation comes about if one tries to manipulate the second 
equation into a form via the substitution: [R][w] = [U]
Which gives:.....

        ([R]    +   [A][R] ) [w]  + [R][w]   +  [A][R][w]   = [0]   (4)
            t             x               t              x       

	Then we get the result:


                         [w]      +     [R]^(-1)[A][R][w]    = [0]    (5)
                            t                            x
Or:
                      \
        [w]       + [ /\ ] [w]   = [0]   
           t                  x         
                  \   
           where [/\] is a diagonal matrix having eigenvalues on its diagonal. 


So the bottom line is can you show equation (3) equals zero.? 
An engineer's way around that is to say [R] is a constant :) but 
since this news group is a math mecca I was hoping to find a more sophiscated
way! 


	Well, thanks in advance!  
	P.S. I hope the tabs and spaces show up as I typed them....



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


	Jim Miller				jhmiller@iastate.edu
	Department of Aerospace                 phone:  515-294-9497
	      Engineering 
	Iowa State University
	(maybe a graduate someday)

	"Failing to plan is planning to fail" - John Atella
	"The roof! The roof! The roof is on fiyah!........"









 	
From: paulm@hpcvra.cv.hp.com (Paul McClellan)
Date: Wed, 23 Dec 1992 17:10:07 GMT
Subject: Re: complex QR-decomposition question
Organization: Hewlett-Packard Co., Corvallis, OR, USA
Newsgroups: sci.math.num-analysis

> 
> I want to calculate the QR-decomposition of a complex matrix with
> only real and positive elements at the main diagonal.
> 
> Is this possible using the householder method?
> 

Yes, using complex arithmetic.
Newsgroups: sci.math.num-analysis
From: steinman@me.utoronto.ca (David Steinman)
Subject: Re: LU decomposition on very large matrix.
Organization: UofT Mechanical Engineering
Distribution: inet
Date: Fri, 25 Dec 1992 20:01:38 GMT

hcobb@fly2.berkeley.edu (Henry J. Cobb) writes:

>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.

Assuming your matrix results from a finite analysis technique, you
should look into an out-of-core skyline matrix solver.  The only
caveat is that i/o time can be of the same order as solve time.  I have a
reference to a published Fortran code, which could be messily ported to 
C via f2c (PD fortran to C converter) or by hand (with lotsa goto's).

    AUTHOR = "G. Dhatt and G. Touzot",
    TITLE = "The finite element method displayed",
    ADDRESS = "Chichester",
    PUBLISHER = "John Wiley \& Sons",
    YEAR = "1984"}

If you go with a skyline solver, you should also consider Sloan's
algorithm, which reorders nodes to minimize the skyline.

    AUTHOR = "S. W. Sloan",
    TITLE = "A fortran program for profile and wavefront reduction",
    JOURNAL = "Int J Num Meth Eng",
    YEAR = "1989",
    VOLUME = "28",
    PAGES = "2651--2679"}

I believe the code provided is in Fortran, but you should be able to 
C it clearly (or, again, use f2c).

If you hear about any C-codes for the above, please let me know.  I'm
not thrilled about being Fortran-dependent for such things.
--
Dave!
From: joshi@kuhub.cc.ukans.edu
Newsgroups: sci.math.num-analysis
Subject: help with NISA/3d FEM program
Date: 29 Dec 92 20:47:11 CST
Organization: University of Kansas Academic Computing Services

Hi there!!
I was wondering if anyone has any experience with NISA/3d
finite element program.  Iw as going to use it to do some
convection analysis for heat transfer.  I need details as
far as support the company offers and the reliability etc.
Any info will help.
thanks,
John

Newsgroups: sci.math.num-analysis
From: steve@eastend.uucp (Steven Roth)
Subject: Re: Numerical Recipes 2nd ed.?
Organization: The East End Computer Ensemble
Date: Mon, 28 Dec 1992 16:21:12 GMT

In article <PHR.92Dec26202406@napa.telebit.com> phr@telebit.com (Paul Rubin) writes:
>
>      I have seen Numerical Recipes for Fortan in the 2nd edition, with
>    updated wavelet algorithms and such, but I was wondering if anyone
>    knows the planned publication schedule for Numerical Recipes in C or
>    Pascal, as there are already example books for the "2nd edition" in C
>    and Pascal.
>
>I've seen the 2nd edition of Numerical Recipes in C at my local bookstore.
>Anyone want to buy my copy of the first edition?
>


Have they improved the program code and added anything new?

-- 

_______________________________________________________________________________

Steven Roth, SysOp, Network Node "EastEnd"      Internet: steve@eastend.jpr.com
Newsgroups: sci.math.num-analysis
From: a722756@roper.mc.ti.com (W. Donald Rolph)
Subject: Re: Natural Convection and FEM
Originator: a722756@roper.mc.ti.com
Keywords: Natural Convection, FEM
Organization: Texas Instruments / Attleboro Mass / USA
Date: Wed, 23 Dec 1992 14:43:21 GMT


In article <a1grvn-@SantaFe.edu>, andy@laguna.santafe.edu (Andy Mell) writes:
|> 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


I always get amused by 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).  I am unsure of the details of your transmission line method,
but the implications are that it is a specific class of FEA.  I would be
interested in more comments (and I will dredge up the journal article!).
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263
Newsgroups: sci.math.num-analysis
From: roth@3d.enet.dec.com (Jim Roth)
Subject: Re: Does this product converge ???
Organization: Digital Equipment Corporation
Date: 23 DEC 92 11:26:20    


In article <1992Dec22.192535.29669@news.eng.convex.com>, Dave Dodson <dodson@convex.COM> writes...
>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.

>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.

But is the limit greater than zero?

Geometrically, this product arises from a nested sequence of
inscribed circles and regular n-gons (convex of course), starting
with a triangle.

- Jim

>Dave Dodson		                             dodson@convex.COM
>Convex Computer Corporation      Richardson, Texas      (214) 497-4234
From: stewart@cs.umd.edu (G. W. Stewart)
Newsgroups: sci.math.num-analysis
Subject: Re: SVD implementation
Date: 25 Dec 92 14:00:16 GMT
Organization: U of Maryland, Dept. of Computer Science, Coll. Pk., MD 20742

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

Newsgroups: sci.math.num-analysis
From: mhosea@seas.smu.edu (Mike Hosea)
Subject: Re: references on integration methods
Organization: SMU - School of Engineering & Applied Science - Dallas
Date: Wed, 30 Dec 1992 05:04:29 GMT

In article <1hppagINNb5f@rave.larc.nasa.gov> makarand@gazelle.larc.nasa.gov (Makarand A. Kulkarni) writes:
>
>Lambert has recently published a book on
>Computational Methods for Systems of Equations.
>(1991). I do not know the publisher and location.
>

Lambert, J.D.,
_Numerical_Methods_for_Ordinary_Differential_Systems_ (The Initial
Value Problem), John Wiley & Sons Ltd., Baffins Lane, Chichester, West
Sussex PO19 1UD, England, 1991.

>
>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)

Runge-Kutta methods of (much) higher orders have also been derived.

>3)Adams-Moulton    : Fourth order accurate

Adams-Moulton formulas exist for all orders.

It is usually best to try to use a polished general-purpose integrator whenever
possible.  It can be replaced with something tailored to the problem later, 
if necessary.  There are some good Runge-Kutta and linear multistep codes on
Netlib (send email to netlib@ornl.gov).
-- 
Regards,
Mike Hosea (mhosea@seas.smu.edu)
From: sshankar@td2cad.intel.com (Sadasivan Shankar)
Newsgroups: sci.math.num-analysis
Subject: Re: Having trouble with FEM functional
Date: 29 Dec 92 18:24:22 GMT
Reply-To: sshankar@td2cad.intel.com (Sadasivan Shankar)
Organization: Intel Corporation, Santa Clara, CA USA

The FEM can be very efficiently used for parabolic equations.  In fact, exhaustive analysis
have been done for parabolic systems. As suggested, the method of lines (space-part by
FEM and time-part by finite differences) is the most common way of doing it.  However, there
are other ways to approach the problem.  For example, the group led by Claes Johnson at
Chalmers University, Sweden have used the so-called space-time formulation for diffusion
equations and have shown that the scheme is of higher-order accuracy (than MOL) and stable.
Refer to papers in Computer Methods in Applied Mechanics and Engineering . In these techniques,
the time-dimension is also approxmated the same way as space-dimension.

S.Shankar
Tech CAD
INTEL
Newsgroups: sci.math.num-analysis
From: engrand@clt13vf.NoSubdomain.NoDomain ()
Subject: question about a reference
Organization: EDF Direction des Etudes et Recherches
Date: Wed, 23 Dec 1992 08:37:15 GMT

Hi,

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)     ?

In particular, does In press stand for International press, is that the name
of the editor ?

Thanks for your help,

Philippe.




Xref: sparky sci.math.num-analysis:3658 alt.sources.wanted:1928
From: lj@mefos.se (Lage Jonsson)
Newsgroups: sci.math.num-analysis,alt.sources.wanted
Subject: C-code for Simplex algorithm wanted
Date: 22 Dec 92 11:24:17 GMT
Organization: MEFOS, Sweden

The subject says it all.

--Lage
Newsgroups: sci.math.num-analysis
From: mhumi@theory.TC.Cornell.EDU (Mayer Humi)
Subject: data filters
Organization: Cornell Theory Center
Date: Sat, 26 Dec 1992 15:00:47 GMT

I am looking for Fortran (or C) program(s) to design various
data filters similar to those that are currentely available
in Matlab and other similar packages. Netlib and IMSL seems to have
nothing in this area .So I shall greatly appreciate your
help in this regard.
 
-----------------------------------------------------------------
address: Prof. Mayer Humi 	     tel:(508)831-5213
         Dept. of Math,WPI,          e-mail:mhumi@wpi.wpi.edu
         100 Institute Rd.           or mhumi@tc.cornell.edu
         Worcester,MA 01609-2247,USA
-----------------------------------------------------------------
From: sitarama@cps.msu.edu (Kocherlakota Sitarama)
Newsgroups: sci.math
Subject: Help on Proofs!
Summary: Help on general proofs.
Date: 22 Dec 92 19:44:28 GMT
Organization: Dept. of Computer Science, Michigan State University
NNTP-Posting-Host: indian.cps.msu.edu
Originator: sitarama@indian.cps.msu.edu

Hello Netters,

I need some good hints on "How to Prove".

If I have to prove something I have the idea. But it seems
that I lack something and my proofs are not good. 
In other words, I have too many verbal statements. Also, when I give my
proof to somebody they won't get my idea after reading it... I will
have to *go explain them* what it is .. and they will say 
"oh... got it".

I think lot of people feel the same way. So those of you who have
some hints, please mail to me and I will summarize.

Zillion Thanks!

Swamy
Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: Gaussian sums
Date: Wed, 30 Dec 1992 15:18:37 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM, T.J. Watson Research Center

>>>>> On 30 Dec 92 13:04:10 GMT, leife@ii.uib.no (Leif Erik R. Hauge) said:


Leif> 	---  GAUSSIAN SUMS ---

Leif> I need to know something about the Gaussian sums.
Leif> What are they?  How are they defined?  To which
Leif> part of math do they belong (algebra? Numb. theory?)

Leif> I would also like to read an easy introduction to the
Leif> theory of Gaussian sums.  Do you know some standard textbooks 
Leif> which give such an introduction?

Leif> Any help appreciated!

Leif> 	Erik

Gauss Sums are essentially fourier transforms of multplicative
characters.  They are quite important in the theory of algebraic
numbers.  There are lots of books that discuss them.  A good book to
start is:

Ireland & Rosen "A Classical Introductions to Modern Number Theory",
Springer Graduate Texts in Math #84.
--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center
Newsgroups: sci.math
From: ags@seaman.cc.purdue.edu (Dave Seaman)
Subject: Re: Measures, and Measurability
Organization: Purdue University
Date: Mon, 21 Dec 1992 14:35:23 GMT

In article <BzM5Jr.47v@mentor.cc.purdue.edu> I write:
> Without looking it up, I would venture to guess that it says if S is a  
> measurable subset of a Euclidean space, then for each epsilon > 0 there  
is  
> a rectangle D such that the measure of (D intersect S), divided by the  
> measure of D, is greater than (1 - epsilon).

Still without looking it up, I would guess that S is required to have  
positive measure (obviously).

--
Dave Seaman
ags@seaman.cc.purdue.edu
From: prener@watson.ibm.com (Dan Prener)
Subject: Re: Education crisis (was RE: how much math...)
Date: Wed, 30 Dec 1992 07:22:05 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
	<PRENER.92Dec12015805@prener.watson.ibm.com>
	<1hr5fjINN972@mirror.digex.com>
Organization: IBM T.J. Watson Research Center, Hawthorne, New York

In article <1hr5fjINN972@mirror.digex.com> kfl@access.digex.com (Keith F. Lynch) writes:

   In article <PRENER.92Dec12015805@prener.watson.ibm.com> prener@watson.ibm.com (Dan Prener) writes:
   > Little kids learn much faster. ...
   > But the fact that little kids' learning capacity is so much greater
   > than that of older people ...

   Is there any evidence for this?  It goes against my experience.

The most commonly cited dramatic example is the ability to learn (natural)
languages.  It is relatively rare for people to acquire the fluency of a
native speaker after childhood.  Lest one think that is because we are not
capable of fluency in more than one language, I hasten to point out that
young children can become fluent in two, and occasionally more, languages
without much difficulty, when exposed to the languages in such a way that
there is little danger of mixing or confusing them.  The standard situation
is where each parent speaks with the child in a different language.

Of course, there are those who believe that young childrens' superiority
at learning language is so dramatic that there must be some other
mechanism at work beyond general learning ability, some switch that 
shuts off the ability to learn languages after a certain age.

So, for another example, less often cited but more dramatic, consider how
much an infant learns in the first year or two of life.  Most of the
informal physics one knows, about the effects of gravity, light, sound,
heat, etc., is learned in that period.  In addition, the complex skills
of hand-eye coordination, upright locomotion, controlled voice production,
are learned then.  So are the philosophical distinctions between self and
other, and the social complexities of communication, even ignoring language.
And on, and on.

Think about the amount one learns as a child not measured in terms of the
number of equivalent academic courses, but in pure information-theoretic
terms: the number of bits of information.  Can you suggest another age
at which that bit rate is higher?


--
                                   Dan Prener (prener@watson.ibm.com)
Newsgroups: sci.math