First-Order Perturbation Theory for Eigenvalues and Eigenvectors

DOI10.1137/19M124784XMaRDI QIDQ5113169

Michael L. Overton, Ren-Cang Li, Anne Greenbaum

Publication date: 3 June 2020

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.00785

zbMATH Keywords

eigenvalueseigenvectorsnumerical linear algebraanalytic perturbation theory

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Perturbation theory of linear operators (47A55)

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Uses Software

• Eigtool
• PSAPSR

Cites Work

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• Analytic perturbation theory for matrices and operators. Licensed ed
• Three methods for refining estimates of invariant subspaces
• Computing stable eigendecompositions of matrices
• Perturbation theory for linear operators.
• On eigenvalues of matrices dependent on a parameter
• Numerical Computing with IEEE Floating Point Arithmetic
• Matrix Algorithms
• On a Perturbation Bound for Invariant Subspaces of Matrices
• Derivatives of Eigenvalues and Eigenvectors of Matrix Functions
• Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix
• Conference on Matrix Computations (Abstracts)
• Perturbation of analytic hermitian matrix functions
• An Efficient Algorithm for Computing the Generalized Null Space Decomposition
• Perturbation Bounds for Matrix Eigenvalues
• Continuation of Invariant Subspaces in Large Bifurcation Problems
• Derivatives and Perturbations of Eigenvectors
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure
• Perturbation Theory for Analytic Matrix Functions: The Semisimple Case
• Continuation of invariant subspaces
• Invariant Subspaces of Matrices with Applications
• Localization Theorems for Nonlinear Eigenvalue Problems
• Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators

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