Large sparse symmetric eigenvalue problems with homogeneous linear constraints: the Lanczos process with inner-outer iterations

We study inner-outer iteration approach for large eigenproblems using the s ymmetric eigenproblem with homogeneous linear constraints as a concrete exa mple. The goal is to compute the extreme eigenvalues to certain accuracy wi th minimum total number of inner iteration steps. We develop two stopping c riteria for the inner-outer Lanczos process: variable-accuracy inner-outer Lanczos process and successive inner-outer Lanczos process, and we provide analysis to explain the behavior of these two inner-outer processes. We als o present various numerical examples to demonstrate the efficiency and accu racy of these approaches. (C) 2000 Elsevier Science Inc. All rights reserve d.