Pseudospectra, critical points and multiple eigenvalues of matrix polynomials

DOI10.1016/j.laa.2008.10.019zbMath1168.15007OpenAlexW1991026314MaRDI QIDQ999799

Rafikul Alam, Sk. Safique Ahmad

Publication date: 10 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.10.019

zbMATH Keywords

multiple eigenvaluematrix polynomialpseudospectrumbackward error

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35) Matrix pencils (15A22)

Related Items (12)

Optimizing the Rayleigh quotient with symmetric constraints and its application to perturbations of structured polynomial eigenvalue problems ⋮ Nearest rank deficient matrix polynomials ⋮ On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations ⋮ Computing nearby non-trivial Smith forms ⋮ Matrix polynomials with specified eigenvalues ⋮ Sensitivity and Backward Perturbation Analysis of Multiparameter Eigenvalue Problems ⋮ Structured eigenvalue condition numbers and linearizations for matrix polynomials ⋮ Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control ⋮ Perturbation analysis for palindromic and anti-palindromic nonlinear eigenvalue problems ⋮ On Householder sets for matrix polynomials ⋮ Backward errors for eigenvalues and eigenvectors of Hermitian, skew-Hermitian,H-even andH-odd matrix polynomials ⋮ Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Palindromic Structures

Uses Software

• Eigtool

Cites Work

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• On the approximation of a bivariate function by the sum of univariate functions
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• On sensitivity of eigenvalues and eigendecompositions of matrices
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• Note on matrices with a very ill-conditioned eigenproblem
• Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications
• On Pseudospectra, Critical Points, and Multiple Eigenvalues of Matrix Pencils
• Generalized Epsilon-Pseudospectra
• Several Concepts to Investigate Strongly Nonnormal Eigenvalue Problems
• On the Pseudospectra of Matrix Polynomials
• On pseudospectra of matrix polynomials and their boundaries

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