HDTenEightyP/NetNews huggingface dataset:
From: suter@fawlty8.eng.monash.edu.au (Mr D. Suter)
Subject: Discretization of Viscosity solutions
Organization: Monash University
Date: Mon, 31 Aug 1992 11:58:32 GMT


I am looking for pointers to work that establishes stability
and convergence tests/properties for finite element
spaces when used to approximate the solution to problems that admit
a viscosity solution (i.e., that parallels the usual results
for elliptic problems).
thanks
d.s.
From: kdorma@ravana.eche.ualberta.ca (Kevin Dorma)
Newsgroups: sci.math.num-analysis
Subject: Re: is there anybody out there, hmmm...
Date: 28 Aug 92 14:14:39 GMT
Organization: Dept. of Chemical Engineering, University of Alberta
X-Newsreader: Tin 1.1 PL3

kdorma@ravana.eche.ualberta.ca (Kevin Dorma) writes:
: How's it goin', eh?
: Say, we have a group for workstation related stuff but nobody has posted

sorry about that, got the wrong newsgroup.

                                  | 
Kevin Dorma                       | Hi, my Lyapunov exponent is 2.31.
kdorma@ravana.eche.ualberta.ca    | What's yours?
Ph.D. type of student             | 
Dept. of Chemical Engineering     | Don't look at my disclaimer, your's
University of Alberta             | is much more interesting.
Edmonton, Alberta                 | 
                                  |
From: herzog@ux5.lbl.gov (Hanan M. Herzog)
Newsgroups: sci.math.num-analysis
Subject: Function to produce pi to infinite precision in C
Followup-To: sci.math.num-analysis
Date: 1 Sep 1992 02:59:03 GMT
Organization: Lawrence Berkeley Laboratory
Distribution: world
NNTP-Posting-Host: ux5.lbl.gov

Hello fellow number-hackers,
	Does anyone know a algorithm in C to produce pi to an "infinite"
precision, printing each decimal, one by one until *I* terminate the
program. I have already gotten basic algorithms to work with double
but a double's max value is limited.

Thanks,

Please reply by email.

Hanan Herzog
From: stewart@cs.umd.edu (G. W. Stewart)
Newsgroups: sci.math.num-analysis
Subject: Re: SW for Canonical Decomposition of Real Skew Symmetric Matrices
Date: 26 Aug 92 04:51:51 GMT
Distribution: sci.math.num-analysis
Organization: U of Maryland, Dept. of Computer Science, Coll. Pk., MD 20742

In article <SMITH.92Aug25085922@minerva.harvard.edu> smith@minerva.harvard.edu (Steven Smith) writes:
>Does there exist (over the net) Fortran or C code for decomposing real
>skew symmetric matrices into canonical form?  I was a little surprised
>when I looked at EISPACK's and LAPACK's indexes and failed to find
>such an algorithm.
>
>Steven Smith

Here is what I have in my bibliography.  As you can see by the citations,
these are secondary sources that I have not read myself.

Pete Stewart

\begin{thebibliography}{1}

\bibitem{govl:89}
G.~H. Golub and C.~F. Van~Loan.
\newblock {\em Matrix Computations}.
\newblock Johns Hopkins University Press, Baltimore, Maryland, 2nd edition,
  1989.

\bibitem{paar:71}
M.~H.~C. Paardekooper.
\newblock An eigenvalue algorithm for skew symmetric matrices.
\newblock {\em Numerische Mathematik}, 17:189--202, 1971.
\newblock Cited in \cite{govl:89}.

\bibitem{vkvd:77}
J.~M. Van~Kats and H.~A. Van~der Vorst.
\newblock Automatic monitoring of {L}anczos schemes for symmetric or
  skew-symmetric generalized eigenvalue problems.
\newblock Technical Report TR 7, Academische Computer Centre, Utrecht, The
  Netherlands, 1977.
\newblock Cited in \cite{govl:89}.

\bibitem{wagr:78}
R.~C. Ward and L.~J. Gray.
\newblock Eigensystem computation for skew-symmetric and a class of symmetric
  matrices.
\newblock {\em {ACM} Transactions on Mathematical Software}, 4:278--285, 1978.
\newblock Cited in \cite{govl:89}.

\end{thebibliography}
Newsgroups: sci.math.num-analysis
From: peter@mr_bun.ccs.uwo.ca (Mr. Peter Budgell)
Subject: Re: Solutions to quartic and cubic eqns.
Organization: University of Western Ontario, London
Date: Wed, 26 Aug 1992 02:23:48 GMT

In article <1992Aug25.161234.13275@magnus.acs.ohio-state.edu>
 kiyer@magnus.acs.ohio-state.edu (Karthik A Iyer) writes:

>Dear fellow nettors,
>	            I am looking for a routine(s) or a place where I can find 
>them (FTP sites, etc) to solve quartic and cubic eqations. I realize that 
>analytic solutions exist, but my problem is that the coefficients of the 
>powers vary by as much as 10-15 orders of magnitude. So, a small error is
>solving the for the cubic's root leads to large errors when that root is
>used to solve for the four roots of the quartic. Any help or leads  would be
>appreciated. I would prefer to get my hands on a FORTRAN double precision 
>routine. Thanks in advance,...


The first of the Graphics Gems books contains routines for quick solution for
the roots of the third and fourth order polynomials.

I don't know if they are accurate when presented with extreme coefficients.
They are coded in C.

The code is by Jochen Schwarze, and the explanation is on page 404 of the text.

"Graphics Gems", ed. Andrew S. Glassner, Academic Press,Inc., Boston, 1990
ISBN 0-12-286165-5
T385.G697

The code can also be found at a few sites in the net.

peter


Newsgroups: sci.math.num-analysis,comp.lang.fortran
From: gropp@godzilla.mcs.anl.gov (William Gropp)
Subject: Re: The importance of high-performance computing
Organization: Argonne National Laboratory, Chicago, Illinois
Date: Wed, 2 Sep 1992 14:51:44 GMT

] Parallel hardware is obviously a way to get revolutionary gains in
] compute power, but Bill Joy's law suggests that single CPUs will give
] tremendous gains without paying any software irritations (they
] certainly have done great in the last five years).
                                   ^^^^^^^^^^^^^^^
This is not true.  What is true is that low end machines (PC's and 
workstations) have made great strides in the last ten years.  The high
end SINGLE PROCESSORS have not.  For example, a single Cray processor has
gone from about 140 Megaflops (Cray 1) to 1000 Megaflops (Cray C-90) in
the last 12 years (these are peak speeds; as such, there is a lot of
room for argument).  If you define a uniprocessor as having a single
set of functional units, the peak gets even lower, as peak clock speeds
have gone from about 12.5 ns (Cray 1) to 2.9 ns (NEC SX-3).  

Bill Gropp
Newsgroups: sci.math.num-analysis
From: skg8286@tamuts.tamu.edu (Srihari Kumar Gangaraj)
Subject: Optimisation without derivatives of function
Organization: Texas A&M University, College Station
Date: Mon, 31 Aug 1992 20:25:59 GMT

	I need help in finding the Global Minimum of a function of n variables
		f = f(x_i) i=1,n
the function f may not be smooth , so I cannot use the standard methods .
The Downhill Simplex Method (or Flexible Polyhedron) in Numerical methods
can give only a minimum and not the Global minimum ( of all the minimum it
picks the minimum neaarest to the guess value).
	Can someone tell if there is any book I can refer to  , or better
thing would be a fortran subroutine available at any of the ftp sites.
	Thank You.
				== Srihari
				  


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

Srihari Gangaraj,
srihari@aero15.tamu.edu                               
Xref: sparky sci.math.num-analysis:2567 comp.lang.fortran:3230
From: elvis@crow.eel.ufl.edu (Ed Deeters)
Subject:  Polygon in or out?
Date: Tue, 25 Aug 92 19:52:04 GMT


Hi, does anyone know a fast way to determine if a point(x,y) is inside or outside
of a polygon when the polygon is defined by n points(x,y) given in a clockwise manner?

thanks for any help 

Bill Deeters
elvis@sioux.ee.ufl.edu
From: tibbits@sisal.llnl.gov (Patrick Tibbits)
Newsgroups: sci.math.num-analysis
Subject: Re: Polygon in or out?
Date: 26 Aug 92 18:55:56 GMT
Organization: Lawrence Livermore National Laboratory

Define vector ai from vertex i to the point p under consideration.
Define vector bi from vertex i to vertex i+1.
Then ai cross bi must be postitive for all i for p to lie within the polygon.


Patrick
Newsgroups: sci.math.num-analysis
From: cbbrowne@csi.uottawa.ca (Christopher Browne)
Subject: Re: *moan*beg*: HELP : sob,snif "forlorn looks", much suffering....
Organization: Dept. of Computer Science, University of Ottawa
Distribution: usa
Date: Mon, 24 Aug 92 01:45:07 GMT

In article <1992Aug23.223610.6707@ecst.csuchico.edu> madams@ecst.csuchico.edu (Michael E. Adams) writes:
>In article <1992Aug23.141644.8398@morrow.stanford.edu> dow@nova2.stanford.edu (Keith Dow) writes:
>>>Given:  p, n, b, & f = 0;  How do you solve for 'i'?
>>>
>>>                            -n                       -n
>>>     100 p  1 - (1 + i/100)^   +  b = -f (1 + i/100)^
>>>            ---------------
>>>                   i
>>
>>Plug in p,n,b and f and you get i can be anthing except zero.  Sounds
>>like a hoax since the problem is trivial.  Since Chico was rated the 
>>number one party school by Playboy...

I wonder what they rated Stanford?  #1 for turkeys?...  And people who
think that i=0 \forall i?

i is NOT anything but zero...

What you'll want to do is probably some sort of Newton's method or a
secant approximation.  It is POSSIBLE that i has a closed-form
representation, but I strongly suspect not.

Reform this so that you get F(i) = 0, thus:

F(i) = 100*p*(1-(1+i/100)^(-n))/i+f*(1+i/100)^(-n)+b

You'll want to find a root (a point where F(i)=0) of this.  There
COULD be multiple roots, and I don't think you can directly solve for
i (Some Mathematica/Maple whiz may contradict me here - but I strongly
doubt it).

I'll not bother doing the program - but will sketch out a quick secant
formula.

(1) Consider the infamous iterative Newton method.  We calculate
successively better (we hope!) approximations of the value at which
F(x) becomes zero.

We start with some estimate of i, say i0= 0.10.

Then, we determine the next estimate, i1, as follows:

i1 = i0 - F(i0)/F'(i0)

F'(i0) is the value of the derivative of F at i0.

i1 will be closer to the answer than i0.

Then, compute i2 = i1 - F(i1)/F'(i1),

and so forth...

in = in-1 - F(in-1)/F'(in-1)

When the two values, in and in-1 get close enough, you can stop.

The unfortunate part here is that this computation requires that you
take the derivative of F, which is somewhat painful.

So, to avoid this, we go to the secant method, which approximates the
derivative.

You'll need to have TWO estimates (say, i0=0 and i1=0.1).

Then, the new estimate, x[n] is computed as follows:

x[n] = x[n-1] - F(x[n-1]) * (x[n-1] - x[n-2])/(F(x[n-1])-F(x[n-2]))

This is somewhat more complicated-looking than Newton's method, and
may not converge as fast, but it certainly should work for your
problem.

I suggest doing NOT doing this in assembly language :-).

There is most probably something in the NETLIB libraries to do this -
but it's simple enough that it's either (a) Trivial to hack up, or (b)
Something you REALLY SHOULD learn to code...

-- 
Christopher Browne
cbbrowne@csi.uottawa.ca
University of Ottawa
Master of System Science Program
Newsgroups: sci.math.num-analysis
From: joep@neon.dfrf.nasa.gov (Joe Pahle)
Subject: Re: MATLAB archives?
Reply-To: joep@neon.dfrf.nasa.gov
Organization: NASA Ames-Dryden FRF, Edwards, CA
Date: Fri, 4 Sep 1992 14:42:16 GMT

In article <sjreeves.920904082952@fourier.ee.eng.auburn.edu>, sjreeves@eng.auburn.edu (Stan Reeves) writes:
|> 
|> Does anyone know of the existence of any Matlab m-file archives for
|> scientific programming?
|> 
|> --
|> Stan Reeves
|> Auburn University, Department of Electrical Engineering, Auburn, AL  36849
|> INTERNET: sjreeves@eng.auburn.edu

Try netlib@ornl.gov or call The Mathworks [508 653 1415] for archives on disk.
There are lots of locally developed m-files for a multitude of tasks, some
don't get in the archive because they are too specific or are still a bit 
"rough". If you can't find a specific desired function, put out a net request!

Joep
Newsgroups: sci.math.num-analysis
From: mihai@nada.kth.se (Mihai Dorobantu)
Subject: older problem
Organization: Royal Institute of Technology, Stockholm, Sweden
Date: Fri, 4 Sep 1992 08:02:26 GMT


Hi,

A few weeks ago there was a request for two functions 
a(x) and b(x) that satisfied some conditions like:

<a(x-n) a(x-m)> = delta(m,n) <b(x-n) b(x-m)> = delta(m,n) 
<a''(x-n) b''(x-m)> = 0 .....

It seems that I misplaced the article at that time and now
it's no longer available among the old articles.

I would much appreciate if anyone could mail me the exact
formulation of the problem.

Many thanks,

Mihai Dorobantu

Dept.for Numerical Analysis and Computer Science
The Royal Institute of Technology, Stockholm - Sweden


Newsgroups: sci.math.num-analysis
From: awhichel@robin.rp.csiro.au (Adrian Whichello)
Subject: predictor corrector methods for ODE's
News-Software: VAX/VMS VNEWS 1.41    
Organization: CSIRO Division of Radiophysics/Australia Telescope National Faci
Date: Wed, 26 Aug 1992 08:38:00 GMT

Dear Netters

	I just read in Numerical Recipes that predictor-corrector methods for
solving initial value ODE's are dead, or at least on their way out. This
strikes me as rather strong, but I would like some other opinions. What do you
think? 
					Adrian P. Whichello
Newsgroups: sci.math.num-analysis
From: patton@phy.uab.edu (David Patton)
Subject: Re: Qubic splines - algorithm needed !!!
Reply-To: patton@phy.uab.edu
Organization: University of Alabama at Birmingham
Date: Tue, 25 Aug 1992 20:56:21 GMT


Try Cubic Splines.  There are many algorithms in netlib, IMSL, and Numerical
Recipes. Not all can handle a data set of non-equidistant points though, so
good luck.
From: gpfrn@cam.nist.gov (Glenn_P._Forney_x6884)
Newsgroups: sci.math.num-analysis
Subject: remapping cfd grid data
Keywords: cfd, grid
Date: 26 Aug 92 13:19:20 GMT
Organization: National Institute of Standards & Technology, Gaithersburg, MD

I have data Tij mapped on a grid (Xi,Yj)
where 1<=i<=n and 1<=j<=m and more importantly the
spacing of grid points is non-uniform.  
Several routines that I have for visualizing this data
assume that the underlying grid has uniform spacing.  i would be
interested in pointers to any routines that would take data defined
on a non-uniform grid and map it to a uniform one.  
thanks,
glenn forney
gpfrn@cfr6.cfr.nist.gov
Xref: sparky sci.math.num-analysis:2560 comp.lang.fortran:3208
From: ajayshah@almaak.usc.edu (Ajay Shah)
Newsgroups: sci.math.num-analysis,comp.lang.fortran
Subject: The importance of high-performance computing
Date: 27 Aug 1992 00:12:31 -0700
Organization: University of Southern California, Los Angeles, CA
NNTP-Posting-Host: almaak.usc.edu

In the Great Lwars, one point which commonly comes up is that fortran
is conceptually lowbrow and hence well-suited for the generation of
good code, esp. to exploit various parallel architectures.

I suspect a modest correction to this viewpoint may be in order in
considering the implications of this fact.  I've spent many years in
scientific computation and generally observed a lot of people at work
firsthand.  It may be a pernicious dataset as I see it, but I know
exactly one person who uses parallel hardware.  Every single person I
know who does scientific computation uses single-CPUs.

Parallel hardware is obviously a way to get revolutionary gains in
compute power, but Bill Joy's law suggests that single CPUs will give
tremendous gains without paying any software irritations (they
certainly have done great in the last five years).

If this is indeed the case; that most people use workstation-type
computers, then the argument changes quite a bit.  There may be room
for a language with simple semantics like fortran, but only for those
5% of users who want to use parallel hardware.  I suspect most
scientific computation out there does not know or care about parallel
hardware.

        -ans.
-- 
Ajay Shah, (213)749-8133, ajayshah@usc.edu
From: rons@hardy.u.washington.edu (Ronald Schoenberg)
Newsgroups: sci.math.num-analysis
Subject: Re: Advice wanted for using C++ in Numerical Analysis
Keywords: object oriented design
Date: 26 Aug 92 14:34:46 GMT
Article-I.D.: u.1992Aug26.143446.1209
Organization: University of Washington, Seattle

In article <BtKpKz.M3F@netnews.jhuapl.edu> pwm@netnews.jhuapl.edu (Miller Phil F1E x8335 ) writes:
.
.
.
>
> Also I would like some advice on the best way to learn
>C++ and object oriented programming with numerical
>simulation in mind.
>

I would recommend starting with Bjarne Stroustrup's _The C++
Programming Language_, 2nd Edition (Addison-Wesley, ISBN
0-201-53992-6, don't waste money on 1st edition).  In my opinion
there are no books that can help with numeric programming in
particular in C++.  S. Lippman's _C++ Primer_ is also good
(Addison-Wesley, ISBN 0-201-16487-6).

The next best thing would be to get some matrix classes.  The best are
those included in the M++ class library.  It is a very extensive set
of classes that essentially turns C++ into a full-featured array
language.  In fact if you've had some experience in array languages
you would be able to start programming at once. It includes LINPACK 
and EISPACK functions.  For more information write, call, or fax

    Dyad Software
    515 - 116th Ave NE, Suite 120
    Bellevue, WA 98004
    (206) 637-9427 (voice)
    (206) 637-9428 (fax)

I would be happy to send anyone some sample M++ code on request.

RogueWave distributes a commercial product that provides a set of matrix and
factorization classes more limited than than M++'s classes.  For more 
information write, call, or fax

   Rogue Wave
   P.O. Box 2328
   Corvallis, OR 97339
   (503) 754-2311 (voice)
   (503) 757-6650

Rogue Wave also distributes a free booklet titled "How C++ Can Make a Better 
FORTRAN".

newmat04 is a public domain class library.  It doesn't have the sophisticated 
memory management of M++, nor the LINPACK/EISPACK functions, but it is free.
This class library would be very usefull for getting started in C++.  It can
be retrieved by anonymous ftp from ftp.uu.net.  It is in the directory
usenet/comp.sources.misc/volume26   
   
Newsgroups: sci.math.num-analysis
From: enzo@research.canon.oz.au (Enzo Liguori)
Subject: REQUEST: constrained optimization of positive definite quadratic form
Organization: Canon Information Systems Research Australia
Date: Tue, 1 Sep 1992 03:39:49 GMT

I'd like suggestions on how to minimize a positive definite quadratic form with
the variable constrained to be within an interval like:
A<=Xi<=B
with A,B constants and Xi any variable of the quadratic form.
If there's a faster algorithm that works with simpler constraints like:
Xi<=0
Xj>=0
Xk unconstrained
that'll probably do.
Thanks in advance.

        Enzo

Enzo Liguori - Canon Information Systems Research Australia
Newsgroups: sci.math.num-analysis
From: takriti@engin.umich.edu (samer Takriti)
Subject: Re: Optimisation without derivatives of function
Date: Tue, 01 Sep 92 09:55:06 EDT
Organization: University of Michigan Engineering, Ann Arbor

In article <1992Aug31.202559.29383@tamsun.tamu.edu> skg8286@tamuts.tamu.edu (Srihari Kumar Gangaraj) writes:
>	I need help in finding the Global Minimum of a function of n variables
>		f = f(x_i) i=1,n
>the function f may not be smooth , so I cannot use the standard methods .
>The Downhill Simplex Method (or Flexible Polyhedron) in Numerical methods
>can give only a minimum and not the Global minimum ( of all the minimum it
>picks the minimum neaarest to the guess value).
>	Can someone tell if there is any book I can refer to  , or better
>thing would be a fortran subroutine available at any of the ftp sites.
>	Thank You.
>				== Srihari
>				  
>
>
>------------------------------------------------------------------------------
>
>Srihari Gangaraj,
>srihari@aero15.tamu.edu                               

There is no method of finding a global minimum of a general function.
The only way is to try an exhaustive search on the region of x (if
possible).
A book on this topic is: Nonlinear Programming, theory and algorithms,
by Bazraa and Shetty.
-Samer
From: mfcrane@vax1.tcd.ie
Subject: laplace transforms and fem in plate vibns
Organization: Trinity College Dublin
Date: Fri, 28 Aug 1992 16:16:33 GMT

Hi Out there,

Heres a problem which has been bugging me for a while now:

Starting off with the undamped biharmonic equation for a vibrating plate:

d^4w + 2d^4w + d^4w = d^2w
----    ----   ----   ----
dx^4  dx^2dy^2 dy^4   dt^2

has the finite element model

        Kw=lambda Mw

where the mass and stiffness matrices contain inertial and stiffness (resp)
terms corresponding to the physical displacement wi, as well as the slopes
and twists at the corners of the elements.

taking Laplace transforms gives

        {s^2*M + K } L(w)= M*x0*s + M*dx0/dt 

Now for a symmetrical square plate, one would expect a certain amount of 
symmetry in w(t) (=L^-1{L(w)), this is not the case.  While the right hand side
of the above equation is a symmetrical vector (symmetrical about its middle
entries) the left hand side is not.

The reason for this is (IMO) the fact that because of the coordinate system
chosen, the slope terms (in the mass and stiffness matrices) on either sides of the plate would be equal in magnitude
but opposite in sign.

viz

	0 0 0 0 0 0 
	0 1 0 0 0 0
	0 0 0 0 0 0
	0 0 0 0 0 0 
	0 1 0 0 0 0
	0 0 0 0 0 0

the elements marked '1' would have the same displacement term, w, the same
dw/dx term (same direction), but the dw/dy terms would be opposite in sign
because of the +ive x and y directions being  to the right and down resp.


Now the questions:

1.	Should only the terms in the mass matrix which involve the displacements	be multiplied by the s**2 terms? (unlikely)

2.	Should I change the coordinate system in some way? (undesirable)

If anybody has any suggestions, I would appreciate an email.

ta muchly,

Martin Crane
Dept. of Comp. Sci.,
Trinity College,
Dublin 2
(400 years young this year)
Ireland


Newsgroups: sci.math.num-analysis
From: russell@sun.soe.clarkson.edu (David Russell)
Subject: Re: *moan*beg*: HELP : sob,snif "forlorn looks", much suffering....
Organization: Clarkson University
Date: Mon, 24 Aug 1992 00:53:19 GMT

From article <1992Aug23.223610.6707@ecst.csuchico.edu>, by madams@ecst.csuchico.edu (Michael E. Adams):
> In article <1992Aug23.141644.8398@morrow.stanford.edu> dow@nova2.stanford.edu (Keith Dow) writes:
>>>Given:  p, n, b, & f = 0;  How do you solve for 'i'?
>>>
>>>                            -n                       -n
>>>     100 p  1 - (1 + i/100)^   +  b = -f (1 + i/100)^
>>>            ---------------
>>>                   i
>>
>>Plug in p,n,b and f and you get i can be anthing except zero.  Sounds
>>like a hoax since the problem is trivial.  Since Chico was rated the 
>>number one party school by Playboy...
>>
> 
> I would not know about the party thing, I'm more of the rioting kind of guy ;-)
> FYI I finished my degree in 82 and am now just a plain applications programmer
> with a bad case of the "forgets".
> 
> This problem MAY be trivial to you, but I have been unable to solve it.  That's
> why I asked for help.  Why don't you show me what a smart boy you are and
> code the solution into Pascal for me.  I can also read Fortran, C, COBOL,
> BASIC, 80x86 & 680x0 Assembly.  Use what ever you like, your pick. 
> 
> remember: "if you can't say anything nice....."
> 
> -Michael
> -- 
> Hi! I am a .signature virus. Copy me into your .signature to join in!

 Michael, I hope you are not serious, or at least made a mistake in
your original equation.
As you stated, Given:  p, n, b, & f = 0; Pluging these into your
equation you get 0 = 0. It doesn't matter what i is......

Could it be you meant to say....  Given:  p, n, b, & f > 0;
--
David M. Russell, Mechanical Eng. Dept.
Clarkson University, Potsdam, NY 13676
(315) 268-9806 
russell@sun.soe.clarkson.edu