Performance evaluation of the Sakurai-Sugiura method with a block Krylov subspace linear solver for large dense Hermitian-definite generalized eigenvalue problems

Abstract

Contour-integral based eigensolvers have been proposed for efficiently exploiting the performance of massively parallel computational environments. In the algorithms of these methods, inner linear systems need to be solved and its calculation time becomes the most time-consuming part for large-scale problems. In this paper, we consider applying a contour-integral based method to a large dense problem in conjunction with a block Krylov subspace method as an inner linear solver. Comparison of parallel performance with the contour-integral based method with a direct linear solver and a ScaLAPACK's eigensolver is shown using matrices from a practical application.