An asynchronous algorithm on the NetSolve global computing system

The explicitly restarted Arnoldi method (ERAM) allows one to find a few eigenpairs of a large sparse matrix. The multiple explicitly restarted Arnoldi method (MERAM) is a technique based upon a multiple projection of ERAM and accelerates its convergence [N. Emamad, S. Petiton, G. Edjlali, Multiple explicitly restarted Arnoldi method for solving large eigenproblems, SIAM J. Sci. Comput. SJSC 27 (1) (2005) 253-277]. MERAM allows one to update the restarting vector of an ERAM by taking into account the interesting eigen-information obtained by its other ERAM processes. This method is particularly well suited to the GRID-type environments. We present an adaptation of the asynchronous version of MERAM for the NetSolve global computing system. We point out some advantages and limitations of this kind of system to implement the asynchronous hybrid algorithms. We give some results of our experiments and show that we can obtain a good acceleration of the convergence compared to ERAM. These results also show the potential of the MERAM-like hybrid methods for the GRID computing environments.