This is the mail archive of the
gsl-discuss@sources.redhat.com
mailing list for the GSL project.
Re: Eigenvalues of a Hermitian matrix
- To: Andrew W Steiner <asteiner at tonic dot physics dot sunysb dot edu>
- Subject: Re: Eigenvalues of a Hermitian matrix
- From: Brian Gough <bjg at network-theory dot co dot uk>
- Date: Tue, 6 Nov 2001 16:02:21 +0000 (GMT)
- Cc: gsl-discuss at sources dot redhat dot com
- References: <Pine.LNX.4.21.0111060950420.29440-100000@tonic.physics.sunysb.edu>
Andrew W Steiner writes:
> I want to calculate the derivative of a function of the
> eigenvalues of a particular Hermitian matrix and so I need the eigenvalues
> of several matrices whose entries are similar. Is there any way to
> provide an inital guess to the gsl_eigen_herm routine if one is known?
> From my understanding of the algorithm, the answer is no. In that
> case, could anyone suggest an alternative?
If you premultiply your perturbed matrices by V' (where V is the
unitary matrix of unperturbed eigenvectors) they will be close to
diagonal. This might improve the computation of the eigenvalues. The
same applies if you have only a guess for V.
It probably won't make much difference overall, but if it does let me
know.
regards
Brian