Absolute and relative Weyl theorems for generalized eigenvalue problems

DOI10.1016/j.laa.2009.08.001zbMath1186.15017OpenAlexW2079814979MaRDI QIDQ1044601

Yuji Nakatsukasa

Publication date: 18 December 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.2009.08.001

zbMATH Keywords

perturbationgeneralized eigenvalue problemWeyl's theoremHermitian definite pencil

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Matrix pencils (15A22)

Related Items (7)

Spectral estimation for diffusions with random sampling times ⋮ Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems ⋮ Convergence of integration-based methods for the solution of standard and generalized Hermitian eigenvalue problems ⋮ Relative perturbation theory for definite matrix pairs and hyperbolic eigenvalue problem ⋮ New perturbation bounds of partitioned generalized Hermitian eigenvalue problem ⋮ Generalized Multiscale Finite Element Method for the Steady State Linear Boltzmann Equation ⋮ Computational design of innovative mechanical metafilters via adaptive surrogate-based optimization

Uses Software

• JDQR
• JDQZ
• mftoolbox

Cites Work

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• A perturbation bound for definite pencils
• The Lidskii-Mirsky-Wielandt theorem -- additive and multiplicative versions
• Accurate singular values and differential qd algorithms
• On perturbation bounds of generalized eigenvalues for diagonalizable pairs
• Accurate Singular Values of Bidiagonal Matrices
• A Trace Minimization Algorithm for the Generalized Eigenvalue Problem
• Jacobi’s Method is More Accurate than QR
• Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
• Templates for the Solution of Algebraic Eigenvalue Problems
• On perturbations of matrix pencils with real spectra, a revisit
• Functions of Matrices

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