Fast enclosure for all eigenvalues in generalized eigenvalue problems

DOI10.1016/j.cam.2009.11.048zbMath1188.65043OpenAlexW1965749137MaRDI QIDQ848556

Shinya Miyajima

Publication date: 4 March 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.11.048

zbMATH Keywords

error boundgeneralized eigenvalue problemspolynomial eigenvalue problemsguaranteed enclosurenon-Hermitian case

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Roundoff error (65G50) Algorithms with automatic result verification (65G20)

Related Items (6)

Fast enclosure for solutions of Sylvester equations ⋮ A sharp version of Bauer-Fike's theorem ⋮ Unnamed Item ⋮ Verified solutions of delay eigenvalue problems ⋮ Structure-dependent improved Wilson-\(\theta\) method with higher order of accuracy and controllable amplitude decay ⋮ Numerical enclosure for each eigenvalue in generalized eigenvalue problem

Uses Software

• INTLAB
• mctoolbox

Cites Work

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• Accuracy and Stability of Numerical Algorithms
• Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
• Computational error bounds for multiple or nearly multiple eigenvalues
• A simple method for error bounds of eigenvalues of symmetric matrices

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