A refined Jacobi-Davidson method and its correction equation

DOI10.1016/j.camwa.2003.01.018zbMath1073.65029OpenAlexW2008671657MaRDI QIDQ2485413

Zhongxiao Jia, Shaoqiang Feng

Publication date: 4 August 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2003.01.018

zbMATH Keywords

numerical experimentsRayleigh quotientRitz vectorRitz valueCorrection equationRefined eigenvector approximationRefined Jacobi-Davidson method

Mathematics Subject Classification ID

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

Related Items (5)

The least squares and line search in extracting eigenpairs in Jacobi-Davidson method ⋮ Hybrid Iterative Refined Method for Computing a Few Extreme Eigenpairs of a Symmetric Matrix ⋮ On the correction equation of the Jacobi-Davidson method ⋮ Hybrid Iterative Refined Method for Computing a Few Extreme Eigenpairs of a Symmetric Matrix ⋮ A refined harmonic Rayleigh-Ritz procedure and an explicitly restarted refined harmonic Arnoldi algorithm

Uses Software

• JDQZ

Cites Work

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• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems
• Composite orthogonal projection methods for large matrix eigenproblems
• Robust preconditioning of large, sparse, symmetric eigenvalue problems
• A refined subspace iteration algorithm for large sparse eigenproblems
• Some theoretical comparisons of refined Ritz vectors and Ritz vectors
• Using cross-product matrices to compute the SVD
• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• Matrix Algorithms
• Generalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices
• The Davidson Method
• The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Residuals of refined projection methods for large matrix eigenproblems

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