The Convergence of Harmonic Ritz Vectors and Harmonic Ritz Values, Revisited

DOI10.1137/16M106755XzbMath1365.65097arXiv1603.01785MaRDI QIDQ5346746

Gang Wu

Publication date: 29 May 2017

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01785

zbMATH Keywords

convergenceeigenvaluenon-Hermitian matrixRitz vectoreigenpairRitz valueharmonic Ritz valueharmonic Ritz vectorharmonic Rayleigh-Ritz projection methodRayleigh-Ritz projection method

Mathematics Subject Classification ID

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

Related Items (6)

Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems ⋮ Convergence proof of the harmonic Ritz pairs of iterative projection methods with restart strategies for symmetric eigenvalue problems ⋮ On a new variant of Arnoldi method for approximation of eigenpairs ⋮ A new inequality for the Hausdorff distance between spectra of two matrices ⋮ On Inner Iterations of Jacobi--Davidson Type Methods for Large SVD Computations ⋮ A refined bound for the spectral variations of matrices

Uses Software

• JDQR
• JDQZ

Cites Work

• Unnamed Item
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• An analogue of the results of Saad and Stewart for harmonic Ritz vectors
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• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• Matrix Algorithms
• Numerical Methods for Large Eigenvalue Problems
• A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices
• A note on harmonic Ritz values and their reciprocals
• Templates for the Solution of Algebraic 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
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• Harmonic projection methods for large non-symmetric eigenvalue problems
• A generalization of Saad's theorem on Rayleigh-Ritz approximations

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