Structured backward error analysis for sparse polynomial eigenvalue problems

We study a backward error analysis for (structured) polynomial eigenvalue problems in homogeneous form arising in practical applications. The perturbation matrices preserve the sparsity as well as other structures, including symmetry, skew-symmetry, Hermite, skew-Hermite. We construct structured perturbation matrices of minimal Frobenius norm such that an approximate eigenpair is an exact eigenpair of the structured perturbed polynomial eigenvalue problem. This work is a complement of previous work for the polynomial eigenvalue problems in homogeneous form.