A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem

DOI10.1007/s11425-008-0050-yzbMath1179.65039OpenAlexW2030344570MaRDI QIDQ1042819

Zhen Wang, Zhongxiao Jia

Publication date: 7 December 2009

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-008-0050-y

zbMATH Keywords

convergenceeigenvalueeigenvectorJacobi-Davidson methodinexact Rayleigh quotient iterationlarge Hermitian matrixmisconvergencesmallest eigenpairuniform positiveness condition

Mathematics Subject Classification ID

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

Related Items

A convergence analysis of the inexact simplified Jacobi-Davidson algorithm for polynomial eigenvalue problems ⋮ Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems ⋮ On convergence of the inexact Rayleigh quotient iteration with MINRES

Uses Software

• JDQZ
• Harwell-Boeing sparse matrix collection
• JDCG

Cites Work

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• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• The effects of inexact solvers in algorithms for symmetric eigenvalue problems
• Inexact Rayleigh quotient-type methods for eigenvalue computations
• Two-sided and alternating Jacobi-Davidson
• Convergence Analysis of Inexact Rayleigh Quotient Iteration
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Combination of Jacobi–Davidson and conjugate gradients for the partial symmetric eigenproblem
• The convergence of Jacobi–Davidson iterations for Hermitian eigenproblems
• Inexact Inverse Iteration with Variable Shift for Nonsymmetric Generalized Eigenvalue Problems