Recovering from accuracy deterioration in the contour integral-based eigensolver

Abstract

We consider a contour integral-based eigensolver that finds eigenvalues in a given domain and the corresponding eigenvectors of the generalized eigenvalue problem. In the contour integral-based eigensolver, quadrature points are placed in the complex plane in order to approximate the contour integral. When eigenvalues exist near a quadrature point, the accuracy of other eigenvalues is deteriorated. We herein propose a method by which to recover the accuracy of the eigenpairs when eigenvalues exist near a quadrature point. A numerical experiment is conducted in order to verify that the proposed method is efficient.