An Implicitly Restarted Block-Lanczos Method for Large Hermitian Eigenproblems

Lothar Reichel

Kent State University, Department of Mathematical Sciences, Kent, OH 44242


Abstract

irbleigs is an implementation of an implicitly restarted block-Lanczos method for computing a few selected nearby eigenvalues and associated eigenvectors of a large Hermitian matrix A. The desired eigenvalues may be extreme or in the interior of the spectrum. The code only requires the evaluation of matrix-vector products with A. Neither factorization of A nor the solution of linear systems of equations with the matrix A are necessary. This, together with a fairly small storage requirement, makes irbleigs well suited for large-scale problems. We describe irbleigs and discuss comparisons with other available software. This talk presents joint work with James Baglama and Daniela Calvetti.