A key to choose subspace size in implicitly restarted Arnoldi method

Abstract

The implicitly restarted Arnoldi method (IRAM) computes some eigenpairs of large sparse non Hermitian matrices. However, the size of the subspace in this method is chosen empirically. A poor choice of this size could lead to the non-convergence of the method. In this paper we propose a technique to improve the choice of the size of subspace. This approach, called multiple implicitly restarted Arnoldi method with nested subspaces (MIRAMns) is based on the projection of the problem on several nested subspaces instead of a single one. Thus, it takes advantage of several different sized subspaces. MIRAMns updates the restarting vector of an IRAM by taking the eigen-information of interest obtained in all subspaces into account. With almost the same complexity as IRAM, according to our experiments, MIRAMns improves the convergence of IRAM.