Complex moment-based eigensolver coupled with two Krylov subspaces

Abstract

Complex moment-based eigensolvers have been well studied for solving interior eigenvalue problems because of their high parallel efficiency. Recently, as a time-efficient complex moment-based eigensolver, the block SS–CAA method was proposed that is based on the communication-avoiding Arnoldi procedure regarding the high-order complex moments. These complex moment-based eigensolvers, including the block SS–CAA method, usually use with a subspace iteration technique for improving the accuracy. In this paper, we aim to improve the convergence behavior of the block SS–CAA method using a block Arnoldi iteration instead of the subspace iteration. The proposed method is based on a special subspace coupled with two Krylov subspaces: one is for the high-order complex moments, and the other is for the iteration technique. Numerical experiments indicate that the proposed method has a higher convergence rate than the block SS–CAA method and the FEAST eigensolver.