Structured backward error for palindromic polynomial eigenvalue problems

Abstract

A detailed structured backward error analysis for four kinds of palindromic polynomial eigenvalue problems (PPEP) (Sigma(d)(l=0)A(l)lambda(l)) x = 0, A(d-l) = epsilon A(l)(star) for l = 0, 1, ..., left perpendiculard/2right perpendicular, where star is one of the two actions: transpose and conjugate transpose, and epsilon is an element of {+/- 1}. Each of them has its application background with the case star taking transpose and epsilon = 1 attracting a great deal of attention lately because of its application in the fast train modeling. Computable formulas and bounds for the structured backward errors are obtained. The analysis reveals distinctive features of PPEP from general polynomial eigenvalue problems (PEP) investigated by Tisseur (Linear Algebra Appl 309: 339-361, 2000) and by Liu and Wang (Appl Math Comput 165: 405-417, 2005).