Gerschgorin’s theorem for generalized eigenvalue problems in the Euclidean metric

DOI10.1090/S0025-5718-2011-02482-8zbMath1230.15012arXiv1008.1202MaRDI QIDQ3094283

Yuji Nakatsukasa

Publication date: 24 October 2011

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

Full work available at URL: https://arxiv.org/abs/1008.1202

zbMATH Keywords

generalized eigenvalue problemforward error analysisEuclidean metricGerschgorin's theorem

Mathematics Subject Classification ID

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

Related Items

Conservation of the number of the eigenvalues of two-parameter matrix problems in bounded domains under perturbations, A new localization set for generalized eigenvalues, Generalized eigenvalue problem for interval matrices, Solution of the \(k\)-th eigenvalue problem in large-scale electronic structure calculations, On refinement of the generalized Bendixson theorem, GPU acceleration of splitting schemes applied to differential matrix equations, On symmetrizing the ultraspherical spectral method for self-adjoint problems, On the Geršgorin-type localizations for nonlinear eigenvalue problems, Guarantees for Existence of a Best Canonical Polyadic Approximation of a Noisy Low-Rank Tensor, Accurate Computation of Generalized Eigenvalues of Regular SR-BP Pairs

Uses Software

• JDQR
• JDQZ

Cites Work

• On perturbation bounds of generalized eigenvalues for diagonalizable pairs
• Geršgorin-type localizations of generalized eigenvalues
• Gershgorin Theory for the Generalized Eigenvalue Problem Ax = λBx
• Templates for the Solution of Algebraic Eigenvalue Problems
• On perturbations of matrix pencils with real spectra, a revisit
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