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Re: [Help-gsl] Eigen solution of non-symmetric tridiagonal

From: Patrick Alken
Subject: Re: [Help-gsl] Eigen solution of non-symmetric tridiagonal
Date: Thu, 24 Mar 2011 10:02:59 +0100
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv: Gecko/20101208 Lightning/1.0b2 Thunderbird/3.1.7

Yes, LAPACK routines for eigenvalues/eigenvectors are much more advanced than the gsl ones, especially for the non-symmetric cases.

For your particular problem, you would need to use the gsl_eigen_nonsymm routines which handle a general non-symmetric matrix. There are no routines in GSL which specifically handle nonsymmetric tridiagonal matrices. There may be such a routine in LAPACK.


On 03/24/2011 09:24 AM, John Chludzinski wrote:
First, I would consider using LAPACK. I use LAPACK with Cygwin (it one of
the math packages that can be downloaded with Cygwin).

My experience using GSL to extract eigenvalues and vectors has been painful.
I used GSL to do a Cholesky factorization, Householder
similarity transformation,and finally solve for eigenvalues and vectors on a
tridiagonal matrix. On a 4000x4000 matrix the cumulatively time was ~9 hrs.
  On the same (AMD) machine using LAPACK, it took ~3.5 minutes.


2011/3/19 Dr. Mehmet SAHIN<address@hidden>

Dear Sir/Madam,
We try to find eigenvalues and eigenvectors of a non-symmetric tridiagonal
matrix. But we have not found any solution in the GSL subroutines. How can
we use the GSL subroutines to solve eigenvalues of a nonsymmetric
tridiagonal marix?
Our real matrix T has the property that the products of pairs of
offdiagonals T(i,i+1)*T(i+1,i) are all positive. Which subroutine(s) we
should use? Could you help us about solving this problem?


Mehmet SAHIN
Selcuk University
Department of Physics
Konya, Turkey

e-mail: address@hidden

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