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From: trh@ukc.UUCP (T.R.Hopkins)
Newsgroups: net.math
Subject: diagonalization of a matrix
Message-ID: <5116@ukc.UUCP>
Date: Wed, 15-May-85 10:52:05 EDT
Article-I.D.: ukc.5116
Posted: Wed May 15 10:52:05 1985
Date-Received: Sat, 11-May-85 07:36:01 EDT
Distribution: net
Organization: Computing Laboratory, U of Kent at Canterbury, UK
Lines: 41

>
>This is further info. on the diagonalization routine I requested:
>
>The matrix is real and tri-diagonal, unfortunately Idon't think its
>hermetian but that shouldnt affect the diagonalization routine.
>
>I'm trying to simulate atoms in a laser cavity so N will be greater than
>500 hopefully larger.
>
>I hope someone has an efficient routine to run on a VAX,
>
>Thanks,
>
>Ed Dougherty
>
>allegra ! psuvax ! burdvax !edwardd
>
>

In efficiency terms it makes a lot of difference whether

	i) the matrix is symmetric
	ii) you want all the eigenvalues or <25% of them
	iii) you want any of the associated eigenvectors

a good source of algorithms (in ALGOL 60) is Wilkinson & Reinsch
`Handbook for Automatic Computation volume II Linear Algebra'.

Alternatively (if you're willing to stoop as low as f77) there is the
public domain package EISPACK - which we implemented without any
changes to the source on our VAX.


Tim Hopkins,
Computing Laboratory,
University of Kent,
Canterbury CT2 7NF
Kent
U.K.

{ trh@ukc.UUCP }