New backward error bounds of Rayleigh–Ritz projection methods for quadratic eigenvalue problem

Abstract

Rayleigh–Ritz projection is one of the efficient procedures to project a large-scale quadratic eigenvalue problem (QEP) into a small-scale QEP by properly choosing a low-dimensional subspace. One common way for solving the projected QEP is to recast it via linearization. In this paper, we establish bounds for backward errors of approximate eigenpairs of QEP relative to those of a linearization. These bounds give useful information to predict the numerical stability of Rayleigh–Ritz projection eigensolvers followed by a linearization. We present results of numerical experiments that support the predictions of the backward error analysis.