Re: gsl-discuss Digest 6 Oct 2003 06:27:59 -0000 Issue 879

[Reinhold Bader <Reinhold dot Bader at lrz-muenchen dot de>]

gsl-discuss-digest-help@sources.redhat.com wrote:

> Subject:
> generalized eigenvalue problem
> From:
> Harald Wiedemann <wiedemann.harald@litef.de>
> Date:
> Mon, 6 Oct 2003 07:27:05 +0200
> To:
> gsl-discuss@sources.redhat.com
>
>
> Hello everybody,
>
> what is the easiest way to calculate the eigenvectors/eigenvalues
> of the generalized eigenvalue problem
>
>      A x = alpha B x
> A, B  = real symmetric matrices
> alpha = eigenvalue
> x  = eigenvector?


I'd recommend using the DSYGVD routine from LAPACK. The divide and
conquer algorithm may have trouble with numerical stability sometimes,
so you might want to check against the results from DSYGV if
there are problems.
Note that B needs to be positive definite in addition to being
symmetric in the above routines since the algorithm attempts
to calculate the matrix square root of B.

If you want to call from C, you might want to use the clapack package
(f2c'ed from Fortran).

LAPACK and clapack are available from http://www.netlib.org


> Thanks in advance,
>
> Harald Wiedemann


--
 Dr. Reinhold Bader

 Leibniz-Rechenzentrum, Abt. Hochleistungssysteme | Tel. +49 89 289 28825
 Barerstr. 21, 80333 Muenchen                     | email Bader@lrz.de