A simultaneous coordinate relaxation algorithm for large, sparse matrix eigenvalue problems

Abstract

An algorithm is proposed for a scheme of simultaneous coordinate relaxation. A variant of root-shifting coordinate relaxation, this procedure consists of iterating several vectors at the same time, instead of one at a time. Results of application of the algorithm to test matrices are discussed. For many matrix eigenvalue problems for which coordinate relaxation is a viable approach, the present algorithm is more effective than previous implementations of coordinate relaxation. Total central processor operations should be decreased due to significantly improved convergence.