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Structured backward error analysis for sparse polynomial eigenvalue problems

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
219
Issue
6
Identifiers
DOI: 10.1016/j.amc.2012.09.035
Keywords
  • Backward Error
  • Structured Polynomial Eigenvalue Problem
  • Sparsity
  • Zero-Preserved
  • (Skew-)Symmetric
  • (Skew-)Hermitian
  • Homogeneous Form

Abstract

Abstract 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.

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