HDTenEightyP/NetNews huggingface dataset:
From: jac@ds8.scri.fsu.edu (Jim Carr)
Newsgroups: sci.math.num-analysis,sci.math.stat,sci.physics
Subject: Re: HELP: A least-squares problem with nonlinear constraints
Date: 13 Sep 92 18:40:05 GMT
Reply-To: jac@ds8.scri.fsu.edu (Jim Carr)
Followup-To: sci.math.num-analysis
Organization: SCRI, Florida State University

I am far from expert in your particular problem, but you seem to be 
encountering a common problem in numerical analysis.  Perhaps my 
answer will trigger some other replies to your inquiry.

In article <0096060C.3C725B20@uinpla.npl.uiuc.edu> tayloe@uinpla.npl.uiuc.edu (Rex Tayloe) writes:
>

  [... details of actual thesis problem omitted ...]

>    1) Is anyone familiar with the method on p.308 of "Probability and
>Statistics in Particle Physics" by Frodesen et. al? (I dont know the proper
>name of the method).  It works well for most events using the LL hypothesis but
>fails for the LS hypothesis due to the fact that one of the matricies is very
>close to singular and cannot be inverted. What am I doing wrong?

If it is "close" to singular you should get an answer; the problem is with 
its reliability and the warning flags it should raise. 

There are two possible problems: your fit parameters in the LS case are 
not really independent of one another or you have encountered a standard 
problem with large least squares systems.  (A large least-squares matrix 
tends to resemble the Hilbert matrix, which has an inverse but has the 
property of being almost indeterminant when you try to solve it with 
any numerical method on machine with finite precision.)  Everything you 
say seems to argue against the latter problem, unless I missed something 
important.  A look at the error matrix might give some guidance. 

Your trouble with other methods might also be due to a correlation, 
since I gather you use the same description of the fit function in 
all cases.  

>    4) Are there guidelines for a reasonable covariance matrix? I find myself
>looking at the darn thing not being able to tell if it is right (other than the
>diagonal terms are the error**2). Should it be positive definite or something
>like that?  Mine always have a fairly large condition number (~10000-100000) Is
>this a signal of something wrong?

The off-diagonal entries are telling you about correlations in your fit.  If 
they are large, it is because you are trying to fit parameters that are not 
entirely independent of one another.  Your problem in (1) above would imply 
that such a result is likely.  If there is a single large off-diagonal 
entry, that is where your correlation lies.   

You might also try looking at the Chi-square surface in the space of such 
correlated parameters for guidance; a rotation to a better parameterization
could be all you need to get a fit. 

Hope this helps.

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)
From: g5000005@nickel.laurentian.ca
Newsgroups: sci.math.num-analysis
Subject: Wanted: Statistica 3.1 manual
Date: 30 Sep 92 19:06:25 GMT
Organization: Laurentian University

Hello netters!

	I am looking for a manual/book for the statistical analysis program 
called Statistica 3.1 (for DOS). I am currently using VAX/VMS SPSSx but I will
be graduating soon (what time is it now?) and have to decide between SPSS-PC+ 
and Statistica for my PC.

	If anyone has used this package I would be interested to hear your 
comments/criticisms regarding this package.

	Thanks in advance!

Norm
Xref: sparky sci.math.num-analysis:2877 sci.comp-aided:175
From: joe@gauss.engga.uwo.ca (Joe LoVetri)
Newsgroups: sci.math.num-analysis,sci.comp-aided
Subject: Re: FDTD code, anywhere?
Date: 30 Sep 92 12:13:26 GMT
Organization: Dept. of Electrical Engineering, UWO, London, Canada

In article <1992Sep23.090452.6912@sai.vtt.fi>, kimmel@cortex.sai.vtt.fi (Jyrki Kimmel) writes:
|> I am trying to find public domain finite-difference time-domain
|> programs (FDTD) for a future project. I may eventually have to make
|> my own programming in any case, but a starting point could be 
|> an existing code for any application.
|> 
|> Any help is appreciated!
|> 
|> Jyrki
|> -- 
|> Jyrki Kimmel, VTT Medical Engineering Laboratory kimmel@cortex.sai.vtt.fi
|> signature in proposal in peer review phase (PPRP). Proposed motto:
|> "El{m{ on kivaa!" ("Life is fun!")  -Kaisa-Maria, age 3

There is an fdtd code in the EMLIB archive site

	microwave.jpl.nasa.gov (IP adress 128.149.76.31)

see README.DIR file

Joe LoVetri

e-mail: joe@gauss.engga.uwo.ca
Newsgroups: sci.math.num-analysis
From: xu@math.psu.edu (Jinchao Xu)
Subject: Text on Numerical ODE
Reply-To: xu@math.psu.edu
Organization: Dept. of Mathematics, Penn State University
Date: Fri, 2 Oct 1992 04:26:09 GMT

I am looking for a text book on numerical ODE that is appropriate
for a one-semester (math) graduate course.  Any suggestions or 
information on possible new books will be appreciated.

Jinchao Xu
Dept of Math, Penn State
From: ledwards@leland.Stanford.EDU (Laurence James Edwards)
Newsgroups: sci.math.num-analysis
Subject: Re: Points in Polygons
Date: 27 Sep 92 00:15:15 GMT
Distribution: inet
Organization: DSG, Stanford University, CA 94305, USA

In article <cscoging.3.717415284@unpcs1.cs.unp.ac.za>, cscoging@unpcs1.cs.unp.ac.za (Chris Scogings) writes:
|> I've been away and missed the first part of this discussion.  I would be 
|> most obliged if someone could mention some references in this area.

Some references:

"Computational Geometry" by Preparata & Shamos
"Interactive Computer Graphics" by Giloi
"An Introduction to Solid Modeling" by Mantyla
"Computer Graphics: principles and practice" by Foley, van Dam, Feiner, & Hughes

|> Why
|> can't we find a better algorithm than shooting rays all over the place?

I've only run across 3 ways to do the point-in-polygon test: 1) shoot a ray and
count crossings, 2) traverse the boundary of the polygon summing the signed
angles subtended by each segment with respect to the point, if the total angle
is non-zero then the point is inside, 3) represent polygons by a boolean sum of
half-planes, plug the point into the line equations (i.e. ax+by+c) for the half
plane boundaries, if the result is negative (assuming outward pointing normals)
for all of the half planes in any of the polygon's convex subregions then the
point is inside.

3) leads to the simplest code *if* you have your polygons represented as
boolean sums of half-planes and *if* you consider a point on the boundary to be
inside the polygon (if points on the border are considered outside you have to
do some non-trivial special case coding). 2) is generally thought to be the
slowest of the methods.  1) is the most common method but there are some
subtleties to coding an efficient and clean implementation.

In 3), for concave polygons, you don't always have to test all of the
planes making up the polygon, but you could decompose your polygons
into convex sub-polygons for the other 2 methods, which would negate
that advantage.

If you are doing this in floating point and you have no fpu then 1) is probably
faster than 3) since for the most part you are just doing comparisons instead
of floating point multiplications. The tricky part about 1) is when your ray
passes through a vertex of the polygon. The brute force approach (metioned in
all the references) is to pick another ray and try again. Alternatively, if you
are at an edge whose endpoint lies on the ray you can look for the next edge
not parallel to the ray and see if it is on the other side of the ray. This
leads to some very messy special case code. There is a way to implement 1)
cleanly: don't count any edge parallel to the ray, and of those edges with one
endpoint on the ray, only count the ones that lie on a particular (arbitrarily
chosen) side of the ray. Doing 1) this way my code consists of 2 routines
totalling about 40 lines.

Larry Edwards
edwards@sunrise.stanford.edu
From: ywang1@husc8.harvard.edu (Yongkang Wang)
Newsgroups: sci.math.num-analysis
Subject: Help Wanted: Stochastic Dynamic Programming
Date: 4 Oct 92 21:06:48 GMT
Distribution: usa
Organization: Harvard University Science Center

Hi,
I am posting a Latex file showing stochastic dynamic progrmming problem
which I seek helps.  If you are an expert in the field, would you please
email me whatever suggestions or answers you may have.  Thank a lot.

P.S. The Latex file is in the next post.


Cheers
Newsgroups: sci.math.num-analysis
From: barry@arnold.math.ucla.edu (Barry Merriman)
Subject: Re: Programming in F77 .... pointers please ?
Organization: UCLA, Mathematics Department
Date: Sat, 3 Oct 92 23:04:46 GMT

In article <1992Oct1.131136.20604@medtron.medtronic.com> om8941@curry (Orlin  
Melstrand) writes:
> natarsu@mse.ogi.edu (N. Sukumar) writes:
> : 
> : 	Hi ! I'm looking for suitable refs./books that outline
> : good programming (Fortran 77) practices that one "should"
> : follow to develop sound and comprehensible numerical s/w in F77.

There's an old, small (< 100 pages)  book by Kernighan and Ritchie called
'The Elements of Programming Style' (roughly), that contains
timeless advice, succinctly presented, on good programming techniques.

If you followed all their rules (~ 30 of them), you'd be ahead of
99.9% of folks who program.

--
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: ercolessi@uimrl7.mrl.uiuc.edu (furio ercolessi)
Subject: Re: P-dimen min of function, NR in C, powell() - anyone got it to run properly?
Reply-To: ercolessi@uimrl7.mrl.uiuc.edu (furio ercolessi)
Organization: MRL - UIUC
Date: Fri, 2 Oct 1992 04:35:50 GMT

In article <1afig6INNapa@network.ucsd.edu>, jracine@weber.ucsd.edu (Jeff Racine) writes:
|>I am trying to minimize a multidimensional function of 5 arguments
|>without using derivatives. Numerical recipes in C has a routine called
|>powell(). I have it up and running, but one problem remains.
|>  [... description of bug ...]

well the fortran version works (although it's slowwww on my
40-parameters problem).
of course i am not saying this to raise the silly language war,
but rather to suggest that perhaps comparing the two versions
may help in tracking the bug. In fortran it's 40 lines long.
furio
--
Furio Ercolessi
Materials Research Laboratory           |   Intl School for Advanced Studies
Univ. of Illinois at Urbana-Champaign   |   Trieste, Italy
furio@uiuc.edu                          |   furio@sissa.it
From: daffy@vaxc.cc.monash.edu.au
Newsgroups: sci.math.num-analysis
Subject: Min/Max of convex function w/ linear constraints - help wanted
Date: 28 Sep 92 12:19:32 +1000
Organization: Monash University - Australia.

Hi,

I have an everywhere convex function that I want to maximise, subject to linear
constraints.

The function is one of about 1000 variables, with about half as many
constraints as vars.

Does anyone have any pointers to a fast algorithm for this type of problem?  It
is probably one of the easiest to solve numericaly, but I want it done as fast
as possible.


Thanks in anticipation,
Daf.

E-mail resonses would be appreciated.
-- 
-------------------------------------------------------------------------------
Davyd Norris		:	"Strange people physicists... In my opinion
Physics Dept.		:	 those that aren't already dead are in some
Monash University,	:        way very, very sick." - Douglas Adams,
Vic, Australia.		:	 "The Long Dark Tea-time Of The Soul"     
-------------------------------------------------------------------------------
Newsgroups: sci.math
From: oyang@cs.monash.edu.au (Kai Shing O'Yang)
Subject: Graphs and Line graphs question
Organization: Computer Science, Monash University, Australia
Date: Wed, 7 Oct 1992 04:45:06 GMT

Hi,

	I've got a question about line graphs and graphs. If I were given
the adjacency matrix of the line graph of a graph G and also the adjacency
matrix of G, can I uniquely identify G or will I get the automorphism group
of G? (i.e. can I construct the incidence matrix of G?)

Thanks for your help,
Kai
--
- Kai S O'Yang, Dept of Comp Sci, Monash Uni, Clayton VIC 3168, Australia  
- AARNET: oyang@bruce.cs.monash.edu.au         - Voice : +(61) 3 565 5778
					       - FAX :   +(61) 3 565 5146
'If one believes everything from the book, rather have no book.'
Newsgroups: sci.math
From: cs202144@umbc8.umbc.edu (cs202144)
Subject: Re: Roman Numerals
Organization: University of Maryland, Baltimore County Campus
Date: Tue, 6 Oct 1992 22:00:53 GMT

> Some people hypothesize that brackets were put over numbers to symbolize
> multiplication by 1000, hence (V) is 5000.  In fact, since (I) has a faint
> resemblance to M, this could explain the symbol M (rather than the
> traditional explanation that M is the first letter of mille, the latin for a
> thousand; this doesn't hold water, as all the other letters are not initials
> of latin numbers, except possibly C.)
>
> also some neat spinoffs: D, 500, is half of (I), i.e. I).
>
> The romans would probably have found it hard to use numbers higher than 3999
> anyway, at least for the man in the street.  Only imperial tax collectors or
> people like Erasthones would need to use them.

I have never seen that method, but like it better than some I have seen.
BTW, That is EXACTLY my point! If they wanted to find out out much gold
ol'e Ceasar had then 3999 just won't cut it. Would you use the () for every
number that needs to be done or would all the numbers be placed like that
at once and the rest normally?

Xref: sparky sci.math:12414 rec.puzzles:6500 comp.theory:2075
From: markh@csd4.csd.uwm.edu (Mark)
Newsgroups: sci.math,rec.puzzles,comp.theory
Subject: Re: more on .999... = 10.0
Date: 29 Sep 1992 14:51:46 GMT
Organization: Computing Services Division, University of Wisconsin - Milwaukee
Distribution: inet
NNTP-Posting-Host: 129.89.7.4

In article <1a6tc7INNo0u@uwm.edu> markh@csd4.csd.uwm.edu (Mark) writes:
>So ACTUALLY, x differs from 10 by an infinitesimal power of 10 as was pointed
>out above.  Which decimal position it differs in depends on which 9.999...
>you chose, since there's a huge number of distinct 9.999...'s that differ at
>some infinite decimal position but are the same at all finite decimal positions.

In article <1992Sep29.035048.4747@cs.cornell.edu> karr@cs.cornell.edu (David Karr) writes:
>I am tempted to write, "Now we have heard it all."

No you haven't.  The construction above is perfectly consistent, and the view
is perfectly sound.

>In article <1a6tjqINNo19@uwm.edu>, markh@csd4.csd.uwm.edu (Mark) goes on:
>>All models of the real number axioms have infinitesimals in them, except one.
>>So choose any garden variety interpretation of the real number system, it has
>>infinitesimals in it with probability 1.
>
>If you take a random selection of models of real numbers out of the
>many analysis books on my shelf, I believe you will find
>infinitesimals in it with probability 0.

Wrong.  A model is an infinite object, a book is finite.

For that matter, it's an open question whether there even EXISTS a model of
the real number system without infinitesimals in it.  As far as anyone knows,
they all have infinitesimals in them.

>in the eighteenth century and thereabouts, but they also led people to
>"prove" many falsehoods.  I thought they were abandoned for that
>reason.  What twentieth-century models of the real numbers have them?

You must have been asleep for 30 years.  Producing such a model is trivial.

Add a constant object (omega) to the formal system, and add an infinite set
of axioms (omega > 0, omega > 1, omega > 2, ...).  This system is logically
consistent and EQUIVALENT to the real number system, but the object omega is
an infinite real number, and 1/omega is an infinitesimal.
From: charles@capmkt.COM (Charles Neveu)
Newsgroups: sci.math
Subject: Re: Opinions Sought (Why major in math?)
Date: 2 Oct 92 20:20:11 GMT
Organization: Capital Market Technology

My wife majored in Mathematics at Wisconsin. At the time (possibly
still true) the requirements for a degree in Mathematics was 33
credits of mathematics courses beyond calculus; no other "breadth"
requirements, besides those of the School Letters and Science, were
required, as opposed to other departments which required 8 credits of
this, 3 credits of that, etc.  Also, there were perhaps 100 undergrad
math majors in a world-class department. 

She took more history classes than math classes and got a very well
rounded education. Also, blase' as we, the general community of people
who read this news group, may be, the world at large finds a math
degree quite impressive, especially, sadly, for a woman.

Charles Neveu
Neurology Unit
UCBerkeley



Newsgroups: sci.math
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Subject: Re: various number systems
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]
Date: Tue, 29 Sep 1992 14:50:40 GMT

lloyd mitchell (lmitchel@nyx.cs.du.edu) wrote:
: I'm aware of quaternions and perplex numbers.  Are there other number
: systems out there about which I should tell them?

In my last post, I meant to mention Cayley's octonions which
are an extension of the quaternions.  Multiplication is neither
commutative nor associative, but it still distributes over addition.
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: HELP! I got a contradiction!
Date: 1 Oct 92 19:07:41 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: bs@fatima.mitre.org (Robert D. Silverman)

In article <1992Sep26.231346.1912@linus.mitre.org>, bs@fatima (Robert D. Silverman) writes:
>>	e^ic  = -1
>>	e^-ic = -1

>How can one get to be a senior math major and still believe that
>f(a) = f(b) implies a = b????

I'd say you're reading too much into the situation.  We all know that
exp is injective for the reals, so it's a natural slip up to assume that
cancellation applies as formally as the "+ -> x" homomorphism laws do.

The history of mathematics is filled with such wrong formal assumptions,
so falling for them the first time around is no big deal.

In article <cannon.21.717524597@scs.unt.edu>, cannon@scs (Dustin Cannon (Lab 3460)) writes:
>>	I had one of my profs tell me the problem is in taking the log of
>>e^ic, but I didn't quite follow.  Can anyone give me a better explanation.

Since no one seems to be actually answering your question, but are complaining
about the existence of the question, here goes.  Ignore the complaints and
stick to math--you'll be happier for it.

You've discovered the following: logarithms are not well-defined for complex
numbers.  exp(ix)=1 for _any_ value of x that's an integral multiple of 2pi.
So log(1) "=" 0, 2pi, 4pi, -2pi, etc.  Complex logarithms are multiple-valued,
and there's no direct way you can get around that.  Despite Robert Silverman's
complaints about the educational system, I'm pretty certain you're used to
square(2)=square(-2) yet 2!=-2.  But for positive x,y, square(x)=square(y)
implies x=y.  So something similar is going on here.  Namely, for real x,y
exp(x)=exp(y) implies x=y, but for complex x,y, this fails.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Xref: sparky sci.math:12652 sci.physics:15848
From: lizi@ocf.berkeley.edu (Cosma R. Shalizi)
Newsgroups: sci.math,sci.physics
Subject: Re: Another Cute Math Joke  (explanation of)
Date: 3 Oct 1992 09:04:39 GMT
Organization: Vampire Research Group at Berkeley :)
NNTP-Posting-Host: lightning.berkeley.edu
Summary: Forgive me, Father, for I have sined

In article <1992Oct1.233811.8760@lmpsbbs.comm.mot.com> bhv@areaplg2.corp.mot.com (Bronis Vidugiris) writes:
>Hmm.  Well, the reason it's funny is that the joke implies you are
>taking a CROSS product of an elephant and a grape, but the math shows
>a DOT product of an elephant and a grape!
>(if A and B are vectors, |A| * |B| * sin(theta) is one expression for the
				      ^^^
>dot product || -> absolute value, theta is the angle between the vectors).
 ^^^
	Are you QUITE sure of this? |A||B|sin(theta) is the magnitude of
the CROSS product, |A||B|COS(theta) of the DOT product - at least the last
time I looked at my Math CRC. They may have changed things since then.
>
>That's pretty funny :-) :-) :-)
   Indeed.
	Cosma Rohilla Shalizi
	In Real Life: lizi@ocf.berkeley.edu
	larval physicist

-- 
"Some savages are persuaded by the 'natural light' that it is their duty to
 eat people, and even Voltaire's savages, who are led by the voice of reason
 to hold that one should only eat Jesuits, are not wholly satisfactory."
-Bertrand Russell on Rousseau in _A History of Western Philosophy_, p. 694
Newsgroups: sci.math
From: preece@StPaul.c10sd4.NCR.COM (Bently.Preece)
Subject: Re: Z <-> Q formula
Organization: NCR NPD, St. Paul, MN
Date: Tue, 29 Sep 1992 22:33:39 GMT

In article <1992Sep27.085952.7534@Csli.Stanford.EDU> hiraga@Csli.Stanford.EDU
(Yuzuru Hiraga) writes:

># This may be a FAQ, but...

>The set of intergers Z and the set of rationals Q have the same cardinality,
>i.e. there exist a bijection between them.  So we all know that.
>But then, is there a "simple" formula that expresses any such mapping?
>You may use any device you please, but note that the subjective little
>"simple" is the criterion.

>-Yuzuru Hiraga

For the positive integers, let

		F(1)    = 1
		F(2k)   = F(k)+1	(k > 0)
		F(2k+1) = 1 / F(2k)	(k > 0)

For the negative integers k let F(k) = -F(-k).  Let F(0) = 0.

Bently Preece
b.preece@stpaul.ncr.com
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: consequences of the Axiom of Choice
Date: 1 Oct 1992 12:37:26 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu
Keywords: Axiom of choice; Cartesian product

In article <1992Oct1.152704.16387@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>Bertrand Russell used to explain choice this way.  Imagine you are
>blessed with infinitely many pairs of shoes and socks.  You wish to
>choose one of each pair.  With the shoes it is easy:  you could take
>all the left ones, or all the right ones.  But can you choose one sock
>from each pair?  To claim that you can is to assert the axiom of
>choice.

So, let's try to find a good mathematical example to illustrate Russel's
explanation.  Explicitly find a countably infinite set S of (unordered) pairs,
for which a choice function is not obvious.  [More technical details.
The set S should be explicitly and uniquely specified in the language of ZF.
It should be provable in ZF that it is a countable set of pairs.]

An UNCOUNTABLE set of pairs with no obvious choice function is
easy: take the set of ALL pairs of sets of real numbers.
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: aq499@cleveland.Freenet.Edu (Hans Baumgartner)
Newsgroups: sci.math
Subject: Mathematica 2.1 for windows, any good?
Date: 2 Oct 1992 08:00:51 GMT
Organization: Case Western Reserve University, Cleveland, Ohio (USA)
NNTP-Posting-Host: hela.ins.cwru.edu


Hi, I would like to buy the student version of mathematica 2.1 
for windows.  I would like to get some opinions on it.  
With the student price of $169 I don't get coprocessor support
or any upgrades.  

What has your experience been with running it under windows 3.1?
Is it stable, buggy, or a waste  of time?

I have a 486-33 8Mb + 210 MbHD.  Diamond Stealth VRAM 1024x768x256color.

Please respond by e-mail to 
aq499@cleveland.freenet.edu   or
72630.211@compuserve.com

Thanks in Advance,
Hans Baumgartner, UCI-Physics
-- 
Hans Baumgartner, UCLA
E-Mail relay address:
aq499@cleveland.freenet.edu
Newsgroups: sci.math,comp.theory,comp.graphics,comp.sys.mac.apps,comp.sys.mac.misc