Software Availability

There are several pieces of software available for subspace iteration described in this section. EB12 is a routine by Duff and Scott for subspace iteration [143]. It is part of the Harwell Subroutine Library. Given a real unsymmetric matrix, this routine computes the $r$ eigenvalues that have the largest positive real part, the largest (in modulus) negative real part, or the largest modulus, with the option of returning the associated eigenvectors. It can also be used to compute other eigenvalues.

SRRIT is a package by Bai and Stewart for calculating a few eigenvalues with largest modulus for a real nonsymmetric matrix [37]. It also computes an approximate orthonormal basis for the associated invariant subspace. SRRIT is nonproprietary. The template in §7.4.3 is closely modeled on SRRIT.

LOPSI is a package by Stewart and Jennings that uses subspace iteration combined with an oblique projection to compute a few eigenvalues of largest modulus and the corresponding eigenvectors of a large sparse matrix [427]. However, LOPSI is based on eigendecompositions instead of the Schur form, and hence one may expect less accuracy in LOPSI than in SRRIT, especially for ill-conditioned eigenvalue problems.

For more information about this software including how to access it, see the book's homepage ETHOME.