ABLEpack Functionality

ABLEpack implements an adaptive block Lanczos method which extracts eigenvalues or eigentriples. This algorithm approximately solves standard non-Hermitian eigenproblems:

               A x = lambda x         y' A = lambda y'

It can also solve generalized non-Hermitian eigenvalue problems:

               A x = lambda B x       y' A = lambda y' B

by using the shift and invert spectral transformation to reduce them to the following standard eigenvalue problems:

               C x = mu x         z' C = mu z'

where

               C  = inv( A - alpha B ) B
               mu = 1 / ( lambda - alpha )
               z  = ( A - alpha B)' y

The user must specify the minimum number of eigenvalues to find, neig. If shift-and-invert is used, then at least neig eigenvalues clustered around the shift alpha are found.

Pre- and post-processing steps are provided. Pre-processing consists of balancing the matrix and performing a shift and invert spectral transformation, both of which are optional. Post-processing undoes anything done by pre-processing, and finds the left and right eigenvectors and the corresponding errors in terms of residuals.

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This page was last modified on Aug 1, 2000.
Send questions to jankunm@turing.cs.ucdavis.edu.