Subject: degenerate eigenvalue problem

From: "Gavin Tsai" <[email-masked]>
Date: Tue, 27 Jul 1999 17:01:17 -0500

Hi, Everyone:

    Here is one problem for degenerate eigensystem...

I try to diagonalize a real and symmetry matrix by using Jacobi transformation.
The program is from the book "numerical recipes".  It seems does not work for the degenerate eigensystem, the eigenvectors are the linear combination of two degenerate eigenvectors.

Is there any one can give me any suggestion or advice for the degenerate eigensystem?

Thanks!

Gavin Tsai

---

From: Rick Venable <[email-masked]>
Date: Wed, 28 Jul 1999 18:01:27 -0400 (EDT)

On Tue, 27 Jul 1999, Gavin Tsai wrote:
> I try to diagonalize a real and symmetry matrix by using Jacobi
> transformation.  The program is from the book "numerical recipes".  It
> seems does not work for the degenerate eigensystem, the eigenvectors are
> the linear combination of two degenerate eigenvectors. 
> 

While the book "Numerical Recipes" is an excellent teaching and learning
tool, not all of the routines are as robust or efficient as those found
elsewhere.  I recommend a visit to

	http://www.netlib.org

where you will probably find a better routine for diagonalizing a
matrix.

In my own case I observed a 50-fold performance improvement for matrix
inversion by changing from the Numerical Recipes routine to one I
obtained from NETLIB. 

A final note-- the authors of Numerical Recipes have copyrighted the
associated source code, and anyone who redistributes a program using
their code is legally obligated to pay them some royalties.  The NETLIN
code is in the public domain.

--
Rick Venable                  =====\     |=|    "Eschew Obfuscation"
FDA/CBER Biophysics Lab       |____/     |=|
Bethesda, MD  U.S.A.          |   \    / |=|  ( Not an official statement or
[email-masked]          |    \  /  |=|    position of the FDA; for that,
http://www.erols.com/rvenable       \/   |=|    see   http://www.fda.gov  )