Multiple Explicitly Restarted Arnoldi method for solving large eigenproblems

In this paper we propose a new approach for calculating some eigenpairs of large sparse non-Hermitian matrices. This method, called Multiple Explicitly Restarted Arnoldi (MERAM), is particularly well suited for environments that combine different parallel programming paradigms. This technique is based on a multiple use of the Explicitly Restarted Arnoldi method (ERAM) and improves its convergence. This technique is implemented and tested on a distributed environment consisting of two interconnected parallel machines. The MERAM technique is compared with ERAM, and one can notice that the convergence is improved. In some cases, more than a twofold improvement can be seen in MERAM results. We also implemented MERAM on a cluster of workstations. According to our experiments, MERAM converges better than the Explicitly Restarted Block Arnoldi method and, for some matrices, more quickly than the PARPACK package, which implements the Implicitly Restarted Arnoldi method.