Structured perturbation analysis of sparse matrix pencils with s-specified eigenpairs

Abstract

We study the structured backward error analysis of s-specified (1≤s≤n) eigenpairs of n-by-n matrix pencils. The structures we consider include, T-symmetric, T-skew-symmetric, Hermitian, skew-Hermitian, T-even, T-odd, H-even, H-odd, T-palindromic, T-anti-palindromic, H-palindromic, and H-anti-palindromic matrix pencils. Minimal structured perturbations are constructed with respect to Frobenius norm such that s-specified eigenpairs become exact eigenpairs of an appropriately perturbed matrix pencil which preserves sparsity. © 2020 Elsevier Inc.