Backward error bounds for polynomial eigenvalue problem solved by a Rayleigh–Ritz type contour integral-based eigensolver

Abstract

The contour integral-based eigensolvers have attracted much attention in recent years. In this paper, we consider solving a polynomial eigenvalue problem (PEP) by a contour integral-based eigensolver named the Sakurai–Sugiura method with Rayleigh–Ritz projection (SS–RR method). We derive a backward error bound of PEP solved by the SS–RR method. This bound can be used to show the accuracy of the computed approximate eigenpairs of PEP. The accuracy of the derived bounds is demonstrated by several examples.