From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 14344 invoked by alias); 15 Aug 2002 12:57:52 -0000 Mailing-List: contact gsl-discuss-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sources.redhat.com Received: (qmail 14324 invoked from network); 15 Aug 2002 12:57:51 -0000 Received: from unknown (HELO velo.localdomain) (24.220.233.245) by sources.redhat.com with SMTP; 15 Aug 2002 12:57:51 -0000 Received: by velo.localdomain (Postfix, from userid 501) id 472872F315; Thu, 15 Aug 2002 07:53:25 -0500 (CDT) Received: from localhost (localhost [127.0.0.1]) by velo.localdomain (Postfix) with ESMTP id 3AB652F2A6; Thu, 15 Aug 2002 07:53:25 -0500 (CDT) Date: Thu, 15 Aug 2002 05:57:00 -0000 From: Lowell Johnson To: Brian Gough Cc: gsl-discuss@sources.redhat.com Subject: Re: Nonsymmetric eigenvalue problem In-Reply-To: <15706.52507.397741.845037@debian> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-SW-Source: 2002-q3/txt/msg00140.txt.bz2 On Wed, 14 Aug 2002, Brian Gough wrote: > Lowell Johnson writes: > > I notice that GSL doesn't (yet) support the computation of the > > eigenvalues of nonsymmetric matrices. I've started converting my > > Fortran-based Mathieu function code over to C and ran into the > > symmetric eigenvalue limitation in GSL. For my original Fortran > > routines, I used the EISPACK routine RG(), which computes the > > eigenvalues and eigenvectors of a real, general matrix. I was > > hoping to be able to use the GSL eigenvalue routines. I have to > > determine the eigenvalues for four matrices. The one listed above > > is the only nonsymmetric matrix. The GSL routines work great for > > the other three matrices. > > Any comments or suggestions? > > The algorithm for non-symmetric eigenvalues is very complicated, which > is why it wasn't implemented. Maybe there is a simpler algorithm for > handling tridiagonal nonsymmetric matrices though. > > What method does Fayez Alhargan use in the TOMS papers? I've taken a very cursory look at Alhargan's algorithm and it appears to use at least some of the same methods that I've used. I'm not a member of SIAM or ACM, and the accessible technical library doesn't carry much in the way of math journals, so I don't have ready access to the actual paper. But I have downloaded Alhargan's C++ routines. The biggest difference appears to be (and this is something that I hadn't really given much thought to yet) that I use the recurrence relation matrices to solve for multiple characteristic values in one pass, whereas it appears that Alhargan's method computes a single characteristic value at a time. Since my original work required Mathieu functions of many orders, it made sense to compute all characteristic values at once, storing them in an array. But this method may be costly for requests only requiring a single value. So maybe I'll work on combining the two approaches in some way. Regarding the nonsymmetric eigenvalue issue, I've found a routine in EISPACK (FIGI2) that converts a sign-symmetric tridiagonal matrix into a symmetric tridiagonal matrix. The algorithm looks pretty simple, so I'll try to get it going. Thanks. Lowell -- ---------0---------0---------0---------0---------0---------0---------0------ Lowell D. Johnson Linux: Bringing stability, security, and freedom to home and business computing since 1991. www.linux.org