The distance of an eigenvector to a Krylov subspace and the convergence of the Arnoldi method for eigenvalue problems

DOI10.1016/j.laa.2016.04.018zbMath1338.65097OpenAlexW2341107015MaRDI QIDQ286164

Hassane Sadok, Gérard A. Meurant, Mohammed Bellalij

Publication date: 20 May 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2016.04.018

zbMATH Keywords

eigenvalueseigenvectorsRitz valuesArnoldi methodnormal matricesKrylov subspacediagonalizable matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (1)

Varying the \(s\) in your \(s\)-step GMRES

Cites Work

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• On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems
• An analogue of the results of Saad and Stewart for harmonic Ritz vectors
• New convergence results on the global GMRES method for diagonalizable matrices
• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Composite orthogonal projection methods for large matrix eigenproblems
• Some theoretical comparisons of refined Ritz vectors and Ritz vectors
• On investigating GMRES convergence using unitary matrices
• The role eigenvalues play in forming GMRES residual norms with non-normal matrices
• Numerical Methods for Large Eigenvalue Problems
• Further Analysis of the Arnoldi Process for Eigenvalue Problems
• The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors
• The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems
• The principle of minimized iterations in the solution of the matrix eigenvalue problem

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