Resolution of large symmetric eigenproblems on a world wide grid

Abstract

We propose an explicit restarted Lanczos algorithm on a world-wide heterogeneous grid platform. This method computes one or few eigenpairs of a large sparse real symmetric matrix. We take the specificities of computational resources into account and deal with communications over the Internet by means of techniques such as out-of-core and data persistence. We also show that a restarted algorithm and the combination of several paradigms of parallelism are interesting in this context. We perform many experimentations using several parameters related to the Lanczos method and the configuration of the platform. Depending on the number of computed Ritz eigenpairs, the results underline how critical the choice of the dimension of the working subspace is. Moreover, the size of platform has to be scaled to the order of the eigenproblem because of communications over the Internet.