Re: Matrix multiplication

[Joe Ward]

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
 
* 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: 
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Fax: 210-617-5423 ** 
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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| | | | 
===| 
This list is open to everyone. Occasionally, less thoughtful| people 
send inappropriate messages. Please DO NOT COMPLAIN TO| THE POSTMASTER 
about these messages because the postmaster has no| way of controlling them, 
and excessive complaints will result in| termination of the list.| | 
For information about this list, including information about the| problem of 
inappropriate messages and information about how to| unsubscribe, please see 
the web page at| http://jse.stat.ncsu.edu/| 
===| 

Re: matrix multiplication

[Kate Cowles]

Try the following site, created by John Castelloe, a recent PhD recipient
from the Univ. of Iowa:

   http://www.stat.uiowa.edu/~jcaste/cppsem/

You will find here slides and materials from a talk John gave entitled

"Using C++ libraries for matrix calculations and random number generation,
   with a Markov chain Monte Carlo example"




Kate Cowles






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THE POSTMASTER about these messages because the postmaster has no
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Re: Matrix multiplication

[David A. Heiser]

- 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



===
This list is open to everyone.  Occasionally, less thoughtful
people send inappropriate messages.  Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.

For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===