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

Abstract

We study inner–outer iteration approach for large eigenproblems using the symmetric eigenproblem with homogeneous linear constraints as a concrete example. The goal is to compute the extreme eigenvalues to certain accuracy with minimum total number of inner iteration steps. We develop two stopping criteria 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 also present various numerical examples to demonstrate the efficiency and accuracy of these approaches.