Parallel algorithm for computing eigenvalues of very large real symmetric matrices on message passing architectures

Abstract

The response of an airplane to air turbulence and the response of a power system network to a fault in the network are two examples of important types of analyses which require large scale eigenvalue and eigenvector computations. In this paper we present message passing parallel algorithms for computing eigenvalues of very large real symmetric matrices. These algorithms are based upon a simple real symmetric Lanczos recursion, can achieve significant speedups, have very small memory requirements, and can be used to compute a few or many eigenvalues.