Eigenvalue computation with NetSolve global computing system

Abstract

To compute a few eigenpairs of a large sparse matrix we use the hybrid Multiple Explicitly Restarted Arnold! Method (MERAM). This method is a technique based upon a multiple projection of ERAM and accelerates its convergence. The MERAM updates the restarting vector of an ERAM by taking the interesting eigen-information obtained by the other ones into account. This method presents two main levels of parallelism which are intra-ERAM and inter-ERAM processes. The high level parallelism between ERAMs can be exploited by a network of heterogeneous machines. In MERAM the communications inter ERAM processes are totally asynchrcnous. The MERAM is fault tolerant and well adapted to GRID-type environments. In this paper, we propose an algorithm of MERAM for NetSolve global computing system. We point out that this kind of systems and their necessary centralism of the communicating information impose to adapt the concerned algorithms. The presented experiments show that a good acceleration of the convergence compared to ERAM can be obtained. We show that the MERAM-like hybrid methods are well suited for the GRID computing environments. © Springer-Verlag Berlin Heidelberg 2006.