Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems

DOI10.1137/20M1331032zbMath1492.65087arXiv2004.04928OpenAlexW3096986994MaRDI QIDQ5071436

Zhongxiao Jia

Publication date: 21 April 2022

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

Full work available at URL: https://arxiv.org/abs/2004.04928

zbMATH Keywords

eigenvalue problemRitz vectorrefined Ritz vectorharmonic Ritz vectorrefined harmonic Ritz vectorcomputable optimally expanded subspacenon-Krylov subspaceoptimal expansion vectoroptimal subspace expansion

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Uses Software

• JDQR
• JDQZ

Cites Work

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• Some theoretical comparisons of refined Ritz vectors and Ritz vectors
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• Numerical Methods for Large Eigenvalue Problems
• Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
• 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
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
• The Convergence of Harmonic Ritz Vectors and Harmonic Ritz Values, Revisited
• The Lanczos and Conjugate Gradient Algorithms
• Variable Accuracy of Matrix-Vector Products in Projection Methods for Eigencomputation

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