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In article <1992Oct8.125936.56162@qut.edu.au> holmes@qut.edu.au writes:
>I have a large real symetric banded matrix (1000x1000) that I want
>to find the first 30 eigenvectors and eigenvalues for. This matrix
>is singular with the first 6 eigenvalues being 0.
>
>Does anyone know of some fast method that will allow me to
>specify a set number of eigenvalues to extract. I have seen the
>Inverse Power method but how do you find the inverse of a singular
>matrix? If anyone knows of books, papers or code that might help
>could you please post the information to me.
>
>Thanks in Advance
>
>---------------------------------------------------------------
>
>Peter Holmes
>Queensland University of Technology
>Australia
>
>EMAIL:  peterh@lime.eese.qut.edu.au
>---------------------------------------------------------------

The LAPACK functions SSBEVX (single precision) DSBEVX (double
precision) CHBEVX (Hermitian) compute eigenvalues for banded matrices
which may be selected by index (i.e., you may select the 7th through
20th eigenvalue) or by value (i.e., you may select eigenvalues greater
than some number and less than some number).  The eigenvectors are
also selected (or you may choose not to compute them at all).
   Let x be your desired data type, then send the following message to
netlib@research.att.com or to netlib@ornl.gov:

    send xbevx from lapack

>>I have a large real symetric banded matrix (1000x1000) that I want
>>to find the first 30 eigenvectors and eigenvalues for. This matrix
>>is singular with the first 6 eigenvalues being 0.

Have you considered the Lanzcos method?  It is particularly useful
when a few of the largest or smallest eigenvalues/eigenvectors are desired.
It is discussed in chap. 9 of:
G. Golub and C. Van Loan, "Matrix Computations," London or Baltimore,
Johns Hopkins University Press, 1989.
This book is also an excellent general reference for matrix computations.
------------
Dan Simon