Structured backward error for palindromic polynomial eigenvalue problems

A detailed structured backward error analysis for four kinds of Palindromic Polynomial Eigenvalue Problems (PPEP) ( d ∑ l=0 Alλ l ) x = 0, Ad−l = εA ⋆ l for l = 0, 1, . . . , ⌊d/2⌋, where ⋆ is one of the two actions: transpose and conjugate transpose, and ε ∈ {±1}. Each of them has its application background with the case ⋆ taking transpose and ε = 1 attracting a great deal of attention lately because of its application in the fast train modeling. Computable formulas and bounds for the optimal structured backward errors are obtained. The analysis reveals distinctive features of PPEP from the usual Polynomial Eigenvalue Problems (PEP) as investigated by Tisseur (Linear Algebra Appl., 309:339–361, 2000) and by Liu and Wang (Appl. Math. Comput., 165:405–417, 2005).