Newsgroup sci.math.num-analysis 29026

Directory

I am looking for numerical routines to solve the following problem
1) Limited RAM  (< 40 bytes available)
2) Limited Processor (68HC11)
3) Limited Time (real time app)
4) Given a small number of samples (10?) determine if a given frequency
is present.
Before I get a million FFT answers the following is important:  I only
care about 1 frequency and a yes/no threshold detector result would be
OK (though a magnitude would be prefered ;->).  Is there a very
efficient way to solve this?
chuckb

For my high school precalc class, a partner and I have to do a report 
dealing with the number pi.  At some time in the U.S. there was a push by 
some state(s) to legislate a rational value for pi. If anyone has any 
information about this issue or any other info on the number pi, such as 
attempts to find the extent of pi's decimal expansion, I would greatly 
appreciate it. Also I would like it if someone could direct me to 
somewhere where I may be able to find the answers to my questions. 
You can post your information here, but I would prefer that you e-mail me 
at cojomelt@juno.com. Thank you for your time.
---W. Jacarl Melton

Dear net users,
I would like to know if there are good reference books for
sturm sequence (sturm sqquence is for diagonalizing tri-diagonal
matrices).  Thanks in advance.
Regards
HC Lee

In article <329B10DD.41C6@mve.com>, Stephen McCarron  writes:
|> Hi all,
|> 
|> 	I'm looking for as optimal a method as possible of 
|> calculating the best fitting plane over a series of 3-d points.
|> Currently I use Newells method, but am interested in trying
|> some alternative methods. Any help at all would be most
|> appreciated, and as I have infrequent opportunity to read
|> this group if you could e-mail a response that would be great.
|> (stephen@mve.com)
|> 
|> Thanks in advance ,
|> 
|> Stephen McCarron
this problem seems to appear regularly in this group. In the present case
two solutions are obvious:
1) you might write it down as an orthogonal distance problem 
   (sum of squared distances of your points from a plane given e.g.
    in normal form x*d1+y*d2+z*d3+gamma=0, with d1**2+d2**2+d3**2=1
    or some other normalization)
   and solve it using odrpack from netlib.
2) you might do some job of odrpack "by hand" , obtaining a three - parameter
   ordinary least squares problem and plug this into some code for
   doing nonlinear least squares
    e.g. a plane is given by
    the hessian normal form (x,y,z)^Td+gamma=0, d being its normal. d to be
    parameterized as 
    d=(d1,d2,d3)=(cos(phi)sin(psi),cos(phi)cos(psi),sin(phi))
   and gamma a real, i.e. 3 parameters.
The distance**2 of a general point P from  the plane is given by the residual
of a least squares problem and computes as (P^Td+gamma)**2, (^T is transpose)
c-code for nonlinear regression may be found in the book
"Numerical recipes in C" by w.h.press,, b.p. flannery et al,
cambridge university press, and in "a numerical library in C for
scientists and engineers" by h.t.lau, crc press (1996).
a good gauss-newton-code in f77 is "nlscon" in codelib of elib 
(telnet elib.zib-berlin.de, login as elib, no password, step menu
down to library index, there to codelib, there to nlscon,
at the prompt write "preftp". this downloads the code in 
the /pub/anonymous-directory. then logout, ftp the same adress,
(anonymous ftp) and retrieve the code from this directory).
(a bit complicated, but a safe procedure).
hope this helps

  It is possible to define determinant for I+T where T is in Lp with p0
  And Also Von Kock has defined determinant with permutations.
  Mathieu

In article ,
David K. Davis  wrote:
>Stany De Smedt (sdesmedt@is1.bfu.vub.ac.be) wrote:
>: Can anyone tell me where I can find information about infinite dimensional
>: matrices.  More particular I need information about the determinant of
>: such matrices if this exist.  I wonder whether there is a definition of
>: the type.
>: \det(A) = \sum_{\sigma permutation on N} (\sgn(\sigma)) (\product_{i \in
>: N} a_{i,\sigma(i)})
>Well, I can tell you where infinite dimensional matrices are used - in
>Hilbert space. But I have never (or rarely) seen determinants mentioned in
>connection with Hilbert space - which leads me to suspect that they don't
>play a useful role or don't readily generalize to the infinite dimensional
>case. I don't know for sure. But it would be in books on Hilbert space or
>Banach space that you mind find your answer. 
One of the early systematic use of the idea of infinite matrices and
determinants is in the theory of Fredholm equations.  For the symmetric
case, the Hilbert-Schmidt approach for I+K is also used for these.
Another place they occur is in probability, where the characteristic
function of a quadratic form with matrix A in normal random variables
with mean 0 and covariance matrix S is det(I - 2itSA)^{-1/2}.  This is
often done by diagonalization, but I have used the Fredholm approach
to compute in in certain cases, and there are important cases where S
is of the form B-C, C of small rank, where the matrix idea seems to
be necessary.
I believe that matrices of the form I+K, K compact, also occur in
quantum mechanics, and that the determinant is sometimes needed.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558

"Rodney B. Roeber"  wrote:
> 
> Hi,
> 
>    I have written a routine which performs LU decomposition using full
> pivoting.  I note from "Numerical Recipes in C" that there is not a
> clearly established method of determining the best pivot.  Currently, I
> successively find the largest remaining value in the matrix and move it
> to the pivot position.  NR uses implicit pivoting to determine which row
> should be swapped.  Is this method viable for swapping columns also?
> Are there more current methods for determining the pivot?  Thanks.
To the best of my knowledge, the state of the art is "threshold
pivoting"
which is described extremely well in an article by Suhl and Suhl,
"Computing Sparse LU Factorizations for Large-Scale Linear Programming
Bases", ORSA Journal on Computing 2 (1990) 325-- 335.
-------------------------------------------------------
gus gassmann          (Horand.Gassmann@dal.ca)
School of Business Administration, Dalhousie University
Halifax, Nova Scotia, Canada , B3H 1Z5
ph. (902) 494-1844
fax (902) 494-1107
http://ttg.sba.dal.ca/sba/profs/hgassmann/hgassman.html

In article 7tL@spcuna.spc.edu,  davis_d@spcunb.spc.edu (David K. Davis) writes:
>Stany De Smedt (sdesmedt@is1.bfu.vub.ac.be) wrote:
>: Can anyone tell me where I can find information about infinite dimensional
>: matrices.  More particular I need information about the determinant of
>: such matrices if this exist.  I wonder whether there is a definition of
>: the type.
>: \det(A) = \sum_{\sigma permutation on N} (\sgn(\sigma)) (\product_{i \in
>: N} a_{i,\sigma(i)})
>
>Well, I can tell you where infinite dimensional matrices are used - in
>Hilbert space. But I have never (or rarely) seen determinants mentioned in
>connection with Hilbert space - which leads me to suspect that they don't
>play a useful role or don't readily generalize to the infinite dimensional
>case. I don't know for sure. But it would be in books on Hilbert space or
>Banach space that you mind find your answer. 
>
>-Dave D.
>
Or in books on Quantum Field Theory (which is, to first order, the same thing).
A common trick is to write (for an N*N matrix, A)
(det A)^-1 = (2\pi i)^N \int dz dz^* exp(-(z^*,Az))
where z and z^* are N dimensional.
Theis can be generalised to infiinite dimensional spaces where the integral
becomes a functional integral and z and z^* become complex fields.
It's also possible to lose the inverse on det A with the same formula, give or
take a normalisation, and in this case z and z^* are (independent) Grassmann
anticommuting variables.
john

In article ,
sdesmedt@is1.bfu.vub.ac.be (Stany De Smedt) wrote:
> Can anyone tell me where I can find information about infinite dimensional
> matrices.  More particular I need information about the determinant of
> such matrices if this exist.  I wonder whether there is a definition of
> the type.
> \det(A) = \sum_{\sigma permutation on N} (\sgn(\sigma)) (\product_{i \in
> N} a_{i,\sigma(i)})
Some of the very early work in Hilbert spaces involved looking a linear
opreators as infinite matrices.  This didn't turn out to be too furitful. 
I know that Phil Hartman wrote some papers on this subject very early in
his career.  You might look for references to Hartman and Wintner or A
Wintner in the early 50's or late 40's.  
Truman

EPSRC PhD Studentship: 
     Adaptive Estimation of Basins of Attraction 
	for Aircraft Flight Dynamics Analysis 
 Department of Aerospace Engineering and Department
     of Engineering Mathematics, University of Bristol
Applications for a three-year PhD studentship are invited from
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The project is in the area of a new and potentially significant
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The techniques will be applied to aircraft flight dynamics models with
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The Faculty of Engineering at Bristol offers a stimulating
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-----------------------------------------
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Department of Aerospace Engineering 
University of Bristol 
Queens Building 
University Walk
Bristol
BS8 1TR
Tel:	0117 928 9765 
Fax:	0117 925 1154 
-- 
======================================================================
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 Dept of Engineering Maths        email:  a.r.champneys@bristol.ac.uk
 University of Bristol            phone:  (+44) (0)117 928 7510
 Bristol  BS8 1TR  UK             fax:    (+44) (0)117 925 1154
======================================================================
 http://www.fen.bris.ac.uk/engmaths/research/nonlinear/staff/arc.html

In Article ,
 wrote:
>
>Hi,
>        Could any of you please suggest a method for solving linear
>equations involving modulo arithmetic. We are not able to solve these
>using conventional methods because they involve division.
>
>
>Thanks in advance,
>
>Sushma.
>(ysr@grove.ufl.edu)
>(ysr@cise.ufl.edu)
>
>
>
>
Chapter 13 of Young & Gregory is on use of residue arithemtic to solve 
linear equations. Y&G; is dated 1972. I think I have seen a paperback
edition of it. Original was 2 volumes. Ch 13 is in V 2.
There are other references from the same era. This one is a text book.

In Article <583j75$683@hpg30a.csc.cuhk.edu.hk>, hclee@axps1.phy.cuhk.hk (Lee
Hon Chor (kwyu)) wrote:
>Dear net users,
>
>I would like to know if there are good reference books for
>sturm sequence (sturm sqquence is for diagonalizing tri-diagonal
>matrices).  Thanks in advance.
>
>
>
>Regards
>HC Lee
Try Section 37 in Chapter 5 of "The Algebraic Eigenvalue Problem" by 
Wilkinson. A great (classical) reference. 

Michael Haggerty wrote:
> 
> In article <57kvv1$j6o@agate.berkeley.edu>,
> blasirs@franklin.CS.Berkeley.EDU (Robert_S Blasi) writes:
> 
> > [...] I was wondering if anyone else out there could either
> > recommend or disrecommend LAPACK++ based on their experience with
> > it.
> 
[.....elided material.........]
> 
> Having said all that, I still use my heavily-hacked version of
> LAPACK++ in my own work, particularly the MATRIX++ part of it.  I wish
> I knew of a better publicly-available set of numerically-oriented
> matrix/vector classes for C++, but I do not.  In my opinion this is a
> real hole in numerical C++ that is waiting to be filled, and I would
> appreciate more information from anyone who has had good experiences
> with another package.
It takes money and resources to generate well-maintained, quality
software, and to think otherwise is pure fantasy.  There are several
commercial high quality C++ matrix class libraries, Dyad's M++ and
RogueWave's Math.h++, for example, that are in wide use.  
Public domain software like Lapack requires money and resources; we just
pay for it in a different way, i.e., through taxes.  That this 
same method doesn't apply to C++ matrix classes is due to the fact
that a quality C++ matrix class library isn't going to get anyone
tenure.  
> In the medium to long term, I suppose packages based on the new C++
> standard for valarray will be the way to go, but in the meantime
> I think most people `roll their own' vector/matrix classes for working
> in C++.
Most people doing serious work use one of the commercially available
matrix class libraries.  
> 
> Incidentally, there is more information and source code for the above
> packages in the web page of their main author, Roldan Pozo:
>     http://math.nist.gov:80/pozo
> 
> Reactions welcome,
> Michael
> 
> ----------------------------------------------------------------------
> Michael Haggerty
> mhagger@mail.delos.physics.wm.edu
> --
> Michael Haggerty
> mhagger@mail.delos.physics.wm.edu

Another good source is in the Mathematics of Computation, (23), 1969,
"Calculation of Gauss Quadrature Points" by Golub & Welsch. They
describe how the problem can be reduced to finding the eigenvalues of a
tridiagonal matrix.
Kel
Pierre Asselin wrote:
> 
> kesinger@math.ttu.edu (Jake Kesinger) writes:
> 
> >Could someone please comment on whether the following is a (theoretically)
> >valid method of computing the Lobatto points of degree n+1?
 
> Chapter 22 of Abramowitz and Stegun has asymptotic formulas for the
> zeros of orthogonal polynomials that could be used as starting points
> for Newton's method.  (The P'_n are Jacobi polynomials, I believe.)
> Still, that's playing with fire.
> 
> --
> --Pierre Asselin, Westminster, Colorado
>   lpa@netcom.com
>   pa@verano.sba.ca.us
-- 
------------------------------------------------------------------
Kelly Black                     Phone: (603) 862-3587 
Department of Mathematics       FAX: (603) 862-4096
University of New Hampshire     e-mail: black@vidalia.unh.edu
Durham, NH 03824  (USA)         WWW: http://www.math.unh.edu/~black

Has anyone seen a good reference on solving linear ODEs using Greens
Functions????  If so, please e-mail me with the title/author.
Thanks
Perillog@aol.com

Version 1.0 of the ALADDIN matrix and finite element package is available
for general distribution. ALADDIN can be used to solve problems in Structural
Analysis and Dynamics, where matrix and finite element computations are an 
integral component.
The source code and detailed examples may be found at:
    http://www.isr.umd.edu/~austin/aladdin.html
Mark Austin
austin@isr.umd.edu

In article <583j75$683@hpg30a.csc.cuhk.edu.hk>, hclee@axps1.phy.cuhk.hk (Lee Hon Chor (kwyu)) writes:
|> Dear net users,
|> 
|> I would like to know if there are good reference books for
|> sturm sequence (sturm sqquence is for diagonalizing tri-diagonal
|> matrices).  Thanks in advance.
|> 
|> 
|> 
|> Regards
|> HC Lee
hi,
you can find it in Stoer&Bulirsch;, Introduction to Numerical Analysis, 
chapter 5 and 6.

Willieum J. Melton wrote:
> 
> For my high school precalc class, a partner and I have to do a report
> dealing with the number pi.  At some time in the U.S. there was a push by
> some state(s) to legislate a rational value for pi. If anyone has any
> information about this issue or any other info on the number pi, such as
> attempts to find the extent of pi's decimal expansion, I would greatly
> appreciate it. Also I would like it if someone could direct me to
> somewhere where I may be able to find the answers to my questions.
> You can post your information here, but I would prefer that you e-mail me
> at cojomelt@juno.com. Thank you for your time.
> 
> ---W. Jacarl Melton
I have two excellent references for you:
1) "A history of Pi" by Petr Beckmann, 1971, St. Martin's Press
2) "Mathematical Cranks" by Underwood Dudley, 1992, Mathematical
   Assoc. of America
The first one, by Petr Beckmann, is very readable, and traces the
history of Pi from 2000 BC to the present.
The second reference devotes an entire chapter to the attempt by 
Indiana to pass legislation relating to Pi. Contrary to the popular
urban
folklore rumor you heard, that it was an effort to legislate a rational
value for Pi, it actually was one that gave the state the privilege of
using the 'proper value' of Pi for free. This 'proper value' was the
result of a circle squarer's faulty attempt to produce a square whose
area was equal to that of a given circle, using only a compass and 
straight-edge.
Quoting Mr. Dudley:
" The preamble of House Bill No. 246, Indiana State Legislature, 1897
  is:
    A bill for an act introducing a new mathematical truth and offerred
  as a contribution to education to be used only by the state of Indiana
  free of cost by paying any royalties whatever on the same, provided
  it is accepted by the official action of the legislature of 1897."
  Hope I've whetted your interest. It's a fascinating story.
Regards,
phil kenny

Willieum J. Melton wrote:
> 
> For my high school precalc class, a partner and I have to do a report
> dealing with the number pi.  At some time in the U.S. there was a push by
... stuff deleted
There is a book on the history of Pi by Petr Bekkman (or some spelling
like
that).  Check it out.
-- 
Mirko Vukovic, Ph.D   	3075 Hansen Way M/S K-109
Varian Associates	Palo Alto, CA, 94304
415/424-4969		mirko.vukovic@varian.grc.com

hello all,
Am I in correct newsgroup for time series analysis?
Thanx all.
Relpy pls cc:
	steve@sc.mcel.mot.com
Steve

Ronald Schoenberg  writes:
> Public domain software like Lapack requires money and resources; we just
> pay for it in a different way, i.e., through taxes.  That this 
> same method doesn't apply to C++ matrix classes is due to the fact
> that a quality C++ matrix class library isn't going to get anyone
> tenure.  
I don't think anyone got tenure for LAPACK. Most high-quality free software
was either written by people who needed it themselves urgently and then
made it freely available, or by people in publicly funded institutions
as a service to the scientific/engineering community. And I see no reason
why a high-quality matrix library for C++ couldn't be done in the same
way.
I don't see much use for commercial libraries in science. People move
frequently to other places, and work in ever changing collaborations.
Their software must be installable easily on any standard workstation
anywhere, which means that it can rely only on standard software
(like C and Fortran compilers) and on free and portable software.
-- 
-------------------------------------------------------------------------------
Konrad Hinsen                          | E-Mail: hinsen@ibs.ibs.fr
Laboratoire de Dynamique Moleculaire   | Tel.: +33-4.76.88.99.28
Institut de Biologie Structurale       | Fax:  +33-4.76.88.54.94
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38027 Grenoble Cedex 1, France         | Nederlands/Francais
-------------------------------------------------------------------------------

I have a question which is of pratical importance. Your
help will be greatly appreciated.
There are two symmetric positive definite matrices  
	[ A    Bt ]		    [ A    Ct ]
 P =    [	  ]		Q = [	      ]
	[ B    D  ]		    [ C    E  ]
The upper left parts of P and Q are identical. The
dimension of A is  m by m while those of D and E are
n by n;
We want change P to  Q by performing some transformation, 
like
	Q = R * P * R(t) 
Usually, R= I+L, where L is a matrix whose first m rows
are all zero.
In order to maintain the numerical stability, it is
desired the eigenvalues of Q be no less than those of
P (it's easy). Simutaneously, it is required the 
difference between eigenvalues of P and Q be as small 
as possible  in order to make P and Q as close as
possible.
The question is a minimum stablization problem (I am
not sure whether it is a proper name or not): how to 
choose R or how to perform such
transformation in order to minimize the difference 
between eigenvalues of P and Q without losing stability?
( eigenvalue of Q >= eigenvalue of P, at least it holds
for the smallest ones;  minimize (evQ - evP))
Thank you.
Y. T. Qi

	I need to solve the Blasius Equation Numerically for f:
  d
             ff'' + 2 f''' = 0
	With the following Boundary Conditions:
	f(0) = 0; f'(0) = 0; f'(Infinity) = 1
	I do not know Runge-Kutta or Euler's Method so 
	I am in kind of a bind. Any detailed help would be greatly
	appreciated if you could email it to me at:
	mwf1935@mail.poapts.com
th	thanks in advance,   Matt

Ronald Schoenberg wrote:
> 
> 
> [text deleted..................................] There are several
> commercial high quality C++ matrix class libraries, Dyad's M++ and
> RogueWave's Math.h++, for example, that are in wide use.
> 
I've been using M++ at work. It is ok, a little buggy. Anyone has
experience with both M++ and Math.h++? Is Math.h++ a better package
or a worse one?
-- 
Guangliang He
mailto:ghe@superlink.net

On Mon, 2 Dec 1996, Willieum J. Melton wrote:

> dealing with the number pi.  At some time in the U.S. there was a push by 
> some state(s) to legislate a rational value for pi. If anyone has any 

	Oh, this is priceless! This is exactly like government! Image: You see
a person up on a platform at a political debate/speech, say a particularly
well established Republican (or, for my Canadian compatriots, Reform 
Party member): "Let's cut down on wastly extra decimal places that nobody 
uses by making new 'rational Pi value' legislation"!!
Ha! I can just see the next US election: "Vote Al Gore for 3.14" !!
(Yes, I know Gore is a Democrat, but it rhymed, and that makes up for it!)
Niel de Beaudrap
----------------------
jd@cpsc.ucalgary.ca

In article <5817lq$6tg@rs18.hrz.th-darmstadt.de>, spellucci@mathematik.th-darmstadt.de (Peter Spellucci) writes:
|> In article <32A3934C.54AF@flinthills.com>, "Rodney B. Roeber"  writes:
|> |> Hi,
|> |> 
|> |>    I have written a routine which performs LU decomposition using full
|> |> pivoting.  I note from "Numerical Recipes in C" that there is not a
|> |> clearly established method of determining the best pivot.  Currently, I
|> |> successively find the largest remaining value in the matrix and move it
|> |> to the pivot position.  NR uses implicit pivoting to determine which row
|> |> should be swapped.  Is this method viable for swapping columns also? 
|> |> Are there more current methods for determining the pivot?  Thanks.
|> |> 
|> |> Rodney B. Roeber
|> |> roeberr@flinthills.com
|> Yes! rather than moving rows and columns explicitly you may rearrange your 
|> code working with a[p[i]][q[j]] instead of a[i][j], initializing the
|> permutation vectors p and q with the identity p[i]==i and q[j]==j.
|> whether this is faster depends  ...... (I guess : no ).
I can think of at least one case where the explicit swapping 
can be faster:
For very large matrices which involve cache swappings when
the columns are distant. If you use permutation indices
columns are in average quite far distant in memory units and 
many swaps may happen all the time.
If you move the columns, the leftover columns tend to be 
closer and less cache swaps may happen. Those swaps can cost
many more cycles than the flops usually counted in text 
books. 
         Wolfgang
-- 
-----------------------------------------------------
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saswmh@unx.sas.com        SAS Campus Drive R5228
(919) 677-8000 x7612      Cary, NC 27513
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