Multiplicative relative perturbation bounds of eigenvalues for diagonalizable matrices

DOI10.1080/00207160.2011.577891zbMath1248.15017OpenAlexW2054385977MaRDI QIDQ2885532

Sulin Pang, Jianxin Chen, Weiqi Luo

Publication date: 23 May 2012

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2011.577891

zbMATH Keywords

numerical exampleseigenvaluescondition numberFrobenius normdiagonalizable matrices\(2\)-normHoffman-Wielandt-type boundsmultiplicative relative perturbation bounds

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Cites Work

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• Multiplicative perturbation bounds for spectral and singular value decompositions
• Relative perturbation theory. III: More bounds on eigenvalue variation
• A note on unifying absolute and relative perturbation bounds
• Singular values, doubly stochastic matrices, and applications
• The variation of the spectrum of a normal matrix
• The perturbation bounds for eigenvalues of normal matrices
• Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
• A Class of Optimal Polynomials Related to Electric Band-Pass Filters

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