Linearization sensitivity and backward perturbation analysis of multiparameter eigenvalue problems

Abstract

We develop a general framework for the sensitivity and backward perturbation analysis of linear and polynomial MEPs For a general norm on the space of MEPs we define the condition number cond W of a simple eigenvalue of an MEPWand derive three equivalent representations of cond W We also analyze holomorphic perturbation of a simple eigenvalue of W Further we define the backward error W of an approximate eigenvalue of W We determine W and construct an optimal perturbation