External selective orthogonalization for the Lanczos algorithm in distributed memory environments

The k-step explicit restart Lanczos algorithm, LExpRes, for the computation of a few of the extreme eigenpairs of large, usually sparse, symmetric mat rices, computes one eigenpair at a time using a deflation technique in whic h each Lanczos vector generated is orthogonalized against all previously co nverged eigenvectors. The computation of the inner products associated with this external orthogonalization often creates a bottleneck in parallel dis tributed memory environments. In this paper methods are proposed which sign ificantly reduce this computational overhead in LExpRes, thereby effectivel y improving its efficiency. The performances of these methods on the Cray-T 3D and the Cray-T3E are assessed and critically compared with that of the o riginal algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.