Backward errors for eigenvalues and eigenvectors of Hermitian, skew-Hermitian,H-even andH-odd matrix polynomials

DOI10.1080/03081087.2012.746331zbMath1278.65036OpenAlexW1966106758WikidataQ114100619 ScholiaQ114100619MaRDI QIDQ2851013

Volker Mehrmann, Sk. Safique Ahmad

Publication date: 1 October 2013

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2012.746331

zbMATH Keywords

eigenvectornonlinear eigenvalue problemperturbation analysishomogeneous polynomialbackward errorHermitian matrix polynomial\(H\)-even matrix polynomial\(H\)-odd matrix polynomialskew-Hermitian matrix polynomial

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Matrix exponential and similar functions of matrices (15A16)

Related Items (7)

Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis ⋮ Structured perturbation analysis of sparse matrix pencils with \(s\)-specified eigenpairs ⋮ Eigenvalue characterization of some structured matrix pencils under linear perturbation ⋮ Perturbation analysis on matrix pencils for two specified eigenpairs of a semisimple eigenvalue with multiplicity two ⋮ Backward error analysis and inverse eigenvalue problems for Hankel and symmetric-Toeplitz structures ⋮ Structured backward error analysis for sparse polynomial eigenvalue problems ⋮ Perturbation analysis for palindromic and anti-palindromic nonlinear eigenvalue problems

Uses Software

• mctoolbox

Cites Work

• Unnamed Item
• On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations
• Trimmed linearizations for structured matrix polynomials
• Pseudospectra, critical points and multiple eigenvalues of matrix polynomials
• More on pseudospectra for polynomial eigenvalue problems and applications in control theory
• A note on the backward errors for Hermite eigenvalue problems
• Perturbation theory for homogeneous polynomial eigenvalue problems
• Backward error and condition of polynomial eigenvalue problems
• Structured mapping problems for linearly structured matrices
• The Quadratic Eigenvalue Problem
• A numerical method for quadratic eigenvalue problems of gyroscopic systems
• Backward Error of Polynomial Eigenproblems Solved by Linearization
• Structured Backward Errors and Pseudospectra of Structured Matrix Pencils
• Structured Eigenvalue Condition Number and Backward Error of a Class of Polynomial Eigenvalue Problems
• Structured Backward Error and Condition of Generalized Eigenvalue Problems
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Linear Perturbation Theory for Structured Matrix Pencils Arising in Control Theory

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