On pseudospectra of matrix polynomials and their boundaries

DOI10.1090/S0025-5718-07-02005-4zbMath1141.65026arXivmath/0604229OpenAlexW1973465423MaRDI QIDQ5429502

Peter Lancaster, Lyonell Boulton, Panayiotis J. Psarrakos

Publication date: 30 November 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604229

zbMATH Keywords

singular valuesmatrix polynomialspseudospectraperturbation of eigenvaluesboundary tracing algorithms

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Robust stability (93D09) Eigenvalues, singular values, and eigenvectors (15A18) Numerical computation of matrix norms, conditioning, scaling (65F35) Matrices over function rings in one or more variables (15A54)

Related Items (15)

An improved grid method for the computation of the pseudospectra of matrix polynomials ⋮ Pseudospectra of isospectrally reduced matrices ⋮ A smallest singular value method for nonlinear eigenvalue problems ⋮ Distance bounds for prescribed multiple eigenvalues of matrix polynomials ⋮ Spectral approximation of generalized Schrödinger operators via approximation of subwords ⋮ Computing unstructured and structured polynomial pseudospectrum approximations ⋮ Matrix polynomials with specified eigenvalues ⋮ The distance from a matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue ⋮ Perforated strict pseudospectra of Demmel's matrices ⋮ Characterization and construction of the nearest defective matrix via coalescence of pseudospectral components ⋮ On condition numbers of polynomial eigenvalue problems ⋮ A note on the distance bound for pseudospectra of matrix polynomials ⋮ Distance Problems for Hermitian Matrix Pencils with Eigenvalues of Definite Type ⋮ Pseudospectra, critical points and multiple eigenvalues of matrix polynomials ⋮ On Householder sets for matrix polynomials

Cites Work

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• A counterexample for two conjectures about stability
• On the Pseudospectra of Matrix Polynomials

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