HDTenEightyP/NetNews huggingface dataset:
From: fortuna@cs.man.ac.uk (Armando Fortuna)
Newsgroups: sci.math.num-analysis
Subject: Mathematica 2.0 for MS-Windows Help!
Date: 27 Aug 92 10:52:55 GMT
Organization: Dept Computer Science, University of Manchester, U.K.

Hi netters,
A friend of mine has Mathematica 2.0 for MS-Windows. He has been having 
a few problems, and asked me to post this message.

1) It seems that, when a graphic is plotted on the screen, memory is
used, and there seems to be no way to get it back. You have to leave
Mathematica (ie "close" it0, and start again... Is there anyway to
reclaim memory after it has been taken? "Clear" and "ClearAll" do not
work...

2) Sometimes, when Mathematica is told to solve an equation, it crashes.
If you tell it to

Solve[a*x^4+b*x^3+c*x^2+d*x+e==0,x]

you can say good-bye to windows... If crashes just after it beeps, as if saying
that it has evaluated the expression above. Windows freezes, and you have
to *reboot* the machine.

The manual says that the program should be able to "Solve" polynomial
equations up to degree 4, and a few of higher degrees. 

After Mathematica loads its Kernel, there are 4.3 Meg of free (virtual)
RAM.

Plot a few 3D graphics, and you'll soon find yourself with 1 Meg free RAM,
and below that, the program crashes taking the computer along...

We would appreciate any help, and I'll post the answers.

Thanks,
Armando
--
===========================================================================
Armando de Oliveira Fortuna                    E-mail: fortuna@cs.man.ac.uk
Dept. of Computer Science                      Tel.: +44 61 275-6132
University of Manchester                       Fax.: +44 61 275-6204
Oxford Road
Manchester M13 9PL                          "...It works better...
England                                             ...if you plug it in..."
============================================================================
All opinions expressed are mine only! If you think otherwise, think it over!
Newsgroups: sci.math.num-analysis
Subject: Re: *moan*beg*: HELP : sob,snif "forlorn looks", much suffering....
From: madams@ecst.csuchico.edu (Michael E. Adams)
Date: Sun, 23 Aug 1992 22:36:10 GMT
Distribution: usa
Organization: California State University, Chico

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!
Newsgroups: sci.math.num-analysis
From: jonathan@chpc.utexas.edu (Jonathan Thornburg)
Subject: cubic spline (was: Re: Qubic splines - algorithm needed !!!)
Summary: the PCHIP package provides fancier *Hermite* splines
Keywords: spline cubic hermite PCHIP Kahaner Moler Nash
Organization: U of Texas at Austin / Physics Dept / Center for Relativity
Date: Thu, 27 Aug 92 17:43:06 GMT

In the base article of this thread, whose reference I have alas
misplaced, a request is made for code to fit a cubic spline through
a data set of non-equidistant points.

One other point...  If you need a higher degree of smoothness than
the usual cubic spline, you might consider *Hermite* splines.  The
(excellent, superb, ++good, highly recommended) book

        David Kahaner, Cleve Moler, Stephen Nash
        "Numerical Methods and Software"
        Prentice-Hall   1989   0-13-627258-4

discusses Hermite splines, and suggests using the PCHIP package to
manipulate them.  The book comes with Fortran code on floppy disk;
I suspect PCHIP itself can be had separately from netlib et al, but
I'm not sure just how or where.

- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}
Newsgroups: sci.math.num-analysis
From: muyu@burn.Princeton.EDU (Muyu Guo)
Subject: Re: Integration of Step function algorithm/code any?
Originator: news@nimaster
Organization: Princeton University
Date: Fri, 28 Aug 1992 15:03:16 GMT

From article <1992Aug28.011918.22579@harlow.harvard.edu>, by job@head-cfa.harvard.edu (Jeffrey Oliver Breen):
> In article <1992Aug14.040957.16304@Princeton.EDU> muyu@burn.Princeton.EDU (Muyu Guo) writes:
>>I am having trouble doing the integral using either qtrap
>>or qsimp from Numerical Recipes:
>>
>>    b
>>    /
>>    | f(x)dx,      	with a < 1, b > 2
>>    /
>>    a
>>   			and f(x) = 1 (1 <= x <= 2)
>>				 = 0  otherwise
>>
>>For example a=0, b=4 or the like the results were nonsense.
>>
>>Does anyone know if there is a good way to get thru this?
>>Thanks a million for your attention.
> 
> Since f(x) will be one from x=1 to x=2, and this range is included by
> the a<1 and b>2 guarantee, and the function is zero everywhere else,
> then the integral just becomes:
> 
>   2
>  /
>  | 1 dx, otherwise known as 1.  Is there a reason you were trying to
>  /
>  1
> 
> solve this numerically?
> -- 
> +-----------
> | Jeffrey Oliver Breen   Harvard-Smithsonian Center for Astrophysics,
> | (617) 495-7252         60 Garden St., Room B-340, MS 6, Cambridge, MA  02138
> |

I think I should rephrase the original question in the 
definition of f(x):   f(x) = 1 ( a < x1 < x < x2 < b)
			   = 0 otherwise

			   I don't know a prior what  is x1 and x2.

So I was told better use an adaptive algorithm for this. Actually
I can do it even with simple trap routine provided I don't want 
too much accuracy, say, relative error 1e-5 between successive
approximate values of the integral.

-- 
Muyu Guo
Newsgroups: sci.math.num-analysis
From: jja@fnbc.com (Joseph Alotta)
Subject: wanted brent.c from numerical recipes
Keywords: brent, numerical, recipes
Organization: First National Bank Of Chicago, Chicago IL, USA
Date: Thu, 27 Aug 92 19:59:35 GMT

Can someone please email me or post a copy of brent.c
from Numerical Recipes in C.

I seem to have all the others except the one I need.


Thanks,

joe.

--
==============================================================
! joe alotta                                    jja@fnbc.com !                                               
!                                             (312) 732-3439 !
!                                                            !
! "The main thing is to keep the main thing the main thing." !
! Dr. George Sweeney                                         !
==============================================================
Newsgroups: sci.math.num-analysis,comp.lang.fortran
From: steve@hubcap.clemson.edu ("Steve" Stevenson)
Subject: Re: The importance of high-performance computing
Organization: Clemson University
Date: Thu, 27 Aug 1992 12:46:28 GMT

ajayshah@almaak.usc.edu (Ajay Shah) writes:

>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
-- 
===============================================================================
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906
Newsgroups: sci.math.num-analysis
From: kent@patience.Stanford.EDU (Mark Kent)
Subject: Re: Advice wanted for using C++ in Numerical Analysis
Keywords: object oriented design
Reply-To: kent@patience.Stanford.EDU (Mark Kent)
Organization: Stanford University Computer Science Department
Date: Wed, 26 Aug 92 12:25:41 GMT

>>C++ and object oriented programming with numerical
>>simulation in mind.

You should learn the language for what it is before trying
to bend it to do what you want.  I'ld suggest leafing through
"C++ Primer" by Stan Lippman (get the 2nd edition), and then
write yourself a few useful non-numerical programs.  Then
read Chapters 11, 12, 13 of "The C++ programming language"
by Bjarne Stroustrup (2nd edition).  

Then start solving the problems you really want to solve.  After your
first prototype, leaf through "Advanced C++" by James Coplien to
remind yourself that you still have a lot to learn :-)

-mark
Newsgroups: sci.math.num-analysis
From: jonathan@chpc.utexas.edu (Jonathan Thornburg)
Subject: Re: Solutions to quartic and cubic eqns.
Summary: numerical zero-finding is probably more accurate, try ZEROIN
Keywords: quartic cubic quadratic equation zero root ill-condition ZEROIN
Organization: U of Texas at Austin / Physics Dept / Center for Relativity
Date: Thu, 27 Aug 92 17:55:51 GMT

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

Unfortunately, the "classical" closed-form analytical solutions
tend to be quite ill-conditioned, *especially* when the coefficients
are widely varying in magnitude.

I suspect you would get much more accurate results if you simply
used a good numerical zero-finding code to numerically locate the
(a) zero of your quartic/cubic.  (Of course, you still have to be
able to *evaluate* the quartic/cubic, which is itself rather tricky
when the coefficients are so disparate in magnitude.  But that's
still a much easier problem than trying to find the roots directly.)

An excellent zero-finding code is ZEROIN, available from netlib
via

	echo 'send zeroin from fmm' | Mail netlib@ornl.gov

This will get you a Fortran subroutine with all the documentation
you need to use it.  For more details, see either the (excellent,
superb, ++good, highly recommended) book

        G. E. Forsythe, M. A. Malcolm, and C. B. Moler
        "Computer Methods for Mathematical Computations"
        Prentice-Hall, Englewood Cliffs, 1977

or section 9.3 of Numerical Recipes.  Be warned, though, that the
code for ZEROIN given in Numerical Recipes (where it's called ZBRENT)
has been "improved", and is of somewhat lower quality than the
original one you'll get from netlib.

- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}
From: smith@minerva.harvard.edu (Steven Smith)
Newsgroups: sci.math.num-analysis
Subject: Re: SW for Canonical Decomposition of Real Skew Symmetric Matrices
Date: 26 Aug 92 15:52:19 GMT
Article-I.D.: minerva.SMITH.92Aug26105219
Distribution: sci.math.num-analysis
Organization: Harvard Robotics Lab, Harvard University

stewart@cs.umd.edu (G. W. Stewart) writes:
> 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.
> 
> 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.

Thank you very much for the information.  Actually, you preceded
yourself by about twelve hours: last night I obtained your
bibliography from netlib and used it to track down Ward and Gray's
algorithm in ACM-TOMS.

Apparently, the ACM doesn't distribute these old algorithms anymore,
so I had to perform a journal-to-ASCII conversion with our OCR scanner
(and edit and debug for a few hours).  So, I have this program now, it
works great, and I will provide it to anyone else who wants it (I
think(?) this is okay by ACM rules).

Steven Smith
From: exukjb@exu.ericsson.se (ken bell)
Newsgroups: sci.math.num-analysis
Subject: partitioning numbers
Summary: A question
Date: 4 Sep 92 20:44:49 GMT
Organization: Ericsson Network Systems, Inc.


Could anyone direct me to some material in pure mathematics or number theory
which explains the business about "partitioning numbers"?  
------------------------------------------------------------------------------
Kenny Bell                          *        Welcome to Mind Wars
Ericsson Network Systems, Inc       *        ANTHEM BBS 386-7907
P.O. Box 833875                     *        Severity with oneself is heroism.
Richardson, TX 75083-3875           *        --A.G.Sertillanges (France, 1943)
------------------------------------------------------------------------------
From: jonathan@chpc.utexas.edu (Jonathan Thornburg)
Newsgroups: sci.math.num-analysis
Subject: cubic spline (was: Re: Qubic splines - algorithm needed !!!)
Summary: see Forsythe, Malcolm, and Moler, or just "spline from fmm" on netlib
Keywords: spline cubic Forsythe Malcolm Moler SPLINE.F netlib fmm
Date: 27 Aug 92 17:35:58 GMT
Organization: U of Texas at Austin / Physics Dept / Center for Relativity

In the base article of this thread, whose reference I have alas
misplaced, a request is made for code to fit a cubic spline through
a data set of non-equidistant points.

The (excellent, superb, ++good, highly recommended) book

        G. E. Forsythe, M. A. Malcolm, and C. B. Moler
        "Computer Methods for Mathematical Computations"
        Prentice-Hall, Englewood Cliffs, 1977

discusses cubic splines in detail, and contains a Fortran subroutine
which does just what you want.

	echo 'send spline from fmm' | Mail netlib@ornl.gov

will get you a copy.

- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}
From: kramer@hermes.ics.uci.edu (David Kramer)
Subject: Monitoring of Library Codes
Newsgroups: sci.math.num-analysis
Reply-To: kramer@ics.uci.edu (David Kramer)
Organization: Univ. of Calif., Irvine, Info. & Computer Sci. Dept.
Date: 3 Sep 92 21:44:37 GMT

Does anyone know of references to monitoring of the use of library
codes? The newest reference I have is Bailey and Jones from ACM TOMS
1975. I am interested in the frequency of use of different libraries
available in IMSL-type packages.

Thanks
David

kramer@ics.uci.edu

Newsgroups: sci.math.num-analysis
From: enzo@research.canon.oz.au (Enzo Liguori)
Subject: Re: Optimisation without derivatives of function
Organization: Canon Information Systems Research Australia
Date: Thu, 3 Sep 1992 03:15:12 GMT

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

As someone else pointed out already there is no way to find the global minimum
in the case of a general function, except exhaustive search (which is normally
higly unpratical).
However, in most of the cases in real world, a good local minimum is still
valuable. In such cases I would suggest Simulated Annealing (SA) which as got
many advantages:
1) It doesn't get easly fouled by the first local minimum at hand and gives
consistently better results than greedy algorithms (like the Downhill Simplex
Method)	or purely random walks.
2) It doesn't care wether the objective functon is smooth or not. It doesn't
even care wether the function is defined on the set of the real or natural
numbers (it can be a function of points of any sort of abstract search space,
such as the space of the logic functions with a prescribed output).
3) It's quite easy to program (most of the effort is computing the objective
function).
4) It's not extremely fussy regarding its control parameters, although you can
get better results spending some time tuning them.
5) It is statistically guaranteed to find the global optimum (but it can take a
very unpratical time to do that).

There are obviously some drawbacks: it is normally pretty slow, but you should
remember that the problem you are trying to solve it's intrinsicly hard.
You may want to try others methods like Genetic Algorithms (GA), but they are
normally harder to program and to tune, even if they are more easly
parallelizable.
A good introduction to SA is the paper:
S. Kirkpatric, C.D. Gelatt, Jr., and M.P. Vecchi, Optimization by simulated
annealing, Science 220 (4598),671-680(1983)
Regarding GA there is something very basic on the July issue of Scientific
American with even some software described at the end of the magazine plus a
lot of references.
I hope it helps.

          Enzo

>				  
>
>
>------------------------------------------------------------------------------
>
>Srihari Gangaraj,
>srihari@aero15.tamu.edu                               
>

Enzo Liguori - Canon Information Systems Research Australia

Newsgroups: sci.math.num-analysis
From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
Subject: Re: REQUEST: constrained optimization of positive definite quadratic form
Reply-To: thompson@atlas.socsci.umn.edu
Organization: Economics Department, University of Minnesota
Date: Tue, 1 Sep 1992 21:07:22 GMT

enzo@research.canon.oz.au (Enzo Liguori) writes:

>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.

The following might prove helpful:

Jorge J. More and Gerardo Toraldo, "Algorithms for Bound Constrained
Quadratic Programming Problems," Numerische Mathematik 55, 377-400
(1989).

Jorge J. More, "Numerical Solution of Bound Constrained Problems," in
Computational Techniques & Applications: CTAC-87, J. Noye & C.
Fletcher (eds.), North-Holland, 29-37 (1988).

The former deals explicitly with your problem.  The simple nature of
your constraints can be exploited to get better performance than you
are likely to get with a QP algorithm that permits more general
constraints.
--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209
Newsgroups: sci.math.num-analysis
Subject: Re: 100 digit integer division?
From: ecmtwhk@ccu1.aukuni.ac.nz (Thomas Koenig)
Date: Sun, 30 Aug 1992 03:40:49 GMT
Organization: University of Auckland, New Zealand.

Try out GMP, GNU's longint package. It should be available at a friendly
neighbourhood ftp site; written in C.
-- 
Thomas Koenig, ecmtwhk@ccu1.aukuni.ac.nz, ib09@rz.uni-karlsruhe.de
The joy of engineering is to find a straight line on a double logarithmic
diagram.
Newsgroups: sci.math.num-analysis
From: Bj|rn Alsberg <alsberg@math.uio.no>
Subject: VARIMAX in MATLAB
Organization: University of Oslo
Date: Fri, 4 Sep 1992 10:35:12 GMT


  I'm interested in a VARIMAX (or other rotations) programs written in
  MATLAB. 
   Thanks in advance!     


Bjoern Alsberg
alsberg@math.uio.no
From: mccreigh@oasys.dt.navy.mil (William Mccreight)
Newsgroups: sci.math.num-analysis
Subject: Re: Oscillatory Integration?
Date: 3 Sep 92 15:39:35 GMT
Article-I.D.: oasys.24552
Reply-To: mccreigh@oasys.dt.navy.mil (William Mccreight)
Organization: Carderock Division, NSWC, Bethesda, MD

You should try Filon's method, which approximates the slowly-
varying factor by a polynomial and the integrates. One ref isr
Davis ananad rabinowitz, Numerical Integration.
From: muzic@ds2.uh.cwru.edu (Ray Muzic)
Newsgroups: sci.math.num-analysis
Subject: MATLAB memory problems
Date: 25 Aug 92 17:02:05 GMT
Article-I.D.: ds2.muzic.714762125
Organization: Case Western Reserve University, Cleveland, Ohio, (USA)


We have noticed a very undesirable behavior of MATLAB with respect to
memory managment.  This occurs on both Ultrix MATLAB (Ultrix 4.2, MATLAB
3.5f) and VAX/VMS MATLAB (VMS 5.4-3, MATLAB 3.5f).

AS we understand it, for each MATLAB assignment and for every expression or
subexpression, MATLAB allocates memory in which to store the results.
MATLAB, however, does not return the memory to the system until one exits
MATLAB. This in itself is not all that bad as it could conceiveably be done
in the interest of efficiency.  What is unforgivable, however, is that MATLAB
does not re-use this memory!

To see this for yourself, define a 512 by 512 matrix and save it to disk.
Then load the matrix into memory several times.  Between successive loads,
show memory (Ultrix: 'ps -au' or 'vmstat', VMS: 'show memory') allocation
and you will probabaly see it increase with each successive load.

Does anyone else observe this behavior on other platforms?


Ray Muzic
Ed Ellert
Don Johann
Gary Muswick




-- 
* Ray Muzic, Jr., Ph.D. | "I try not to think, it slows the progress." - rfm2 *
* muzic@ds2.uh.cwru.edu | Biomedical Engr, CWRU & Image Analysis Ctr, UH  __o *
* Voice: (216)-844-3543 | Div Nuclear Radiology, Univ Hosp of Cleveland  -\<, *
* Fax: (216)-844-3106   | 2074 Abington Rd, Cleveland, OH, 44106, USA....O/ O *
Newsgroups: sci.math.num-analysis
From: takriti@engin.umich.edu (samer Takriti)
Subject: Re: REQUEST: constrained optimization of positive definite quadratic form
Date: Wed, 02 Sep 92 19:11:15 EDT
Organization: University of Michigan Engineering, Ann Arbor

In article <1992Sep2.155040.14505@mic.ucla.edu> iwelch@agsm.ucla.edu (Ivo Welch) writes:
>Could someone please post code which solves this quadratic programming
>problem, or refer me to a free  source of such code?
>
>Preference: C++, C, Fortran (in descending order).
>
>Thanks.
>
>/ivo welch

Well, there is Lindo and OSL. OSL is written by IBM: Optimization
Subroutine Library. If you have an ibm/6000 station you shoild be
able to run osl. I have no idea if they are free or not.
-Samer