David --
Great message!!
One of most "revealing" numerical analysis
problems is when there is
interest in "POWERING" a transition matrix in a
Markov model.
PRE-MULTIPLYING to "POWER" the matrix
compared to
POST-MULTIPLYING can get quite different
results
This due to the different order of accumulation of
the sum of products of
numbers between 0 and 1.
Numerical analysts can have lots of challenging
problems.
-- Joe
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* Joe Ward Health Careers High School *
* 167 East Arrowhead Dr 4646 Hamilton Wolfe *
* San Antonio, TX 78228-2402 San Antonio, TX 78229 *
* Phone: 210-433-6575 Phone: 210-617-5400 *
* Fax: 210-433-2828 Fax: 210-617-5423 *
* [EMAIL PROTECTED] *
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----- Original Message -----
From: David A. Heiser <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>;
Anthony Pleticos <[EMAIL PROTECTED]>
Sent: Friday, March 17, 2000 2:27 PM
Subject: Re: Matrix
multiplication
| ----- Original Message -----
| From: Anthony Pleticos <[EMAIL PROTECTED]>
| To: <[EMAIL PROTECTED]>
| Sent: Wednesday, March 15, 2000 4:24 PM
| Subject: Matrix multiplication
|
|
| > I don't know if I hit the correct site but would be grateful for an
| answer -
| > it is a fundamental one. We all know that linear regression can be
| > accomplished by matrix multiplication and that there are packages which
| will
| > do it for you. I am teaching myself C++ and for the purposes of the
| > excercise I would like to know how to create a matrix or obtain ready made
| > code (ie "numerical recipe" )class so I could declare in a program:
| >
| > #include <iostream.h>
| > #include <math.h>
| > #include <matrix.h> /* if there is such a file */
| ............................................................................
| ....................
| The basic problem is that there is an enormous differences between real
| world matricies. There is no one method for numerical matrix reductions. For
| example note the very large number of Fortran subroutines that focus on
| peculiar aspects (banded, complex, sparse, near singular, positive definite,
| not positive definate, triangular, rank deficient, etc., etc) Note the large
| number of free Fortran subroutines devoted to matrices in "NETLIB". There
| are other free Fortran libraries available from the web.
|
| Matrix multiplication is not numerically straightforward given a finite
| computer environment. One can get very misleading results doing the standard
| multiply and add method using standard single precision.
|
| I would suggest you get familiar with numerical analysis methods. I
| personally prefer the works of G. W. Stewart as a source.
|
| DAHeiser
|
|
|
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