Two-sided and alternating Jacobi-Davidson

DOI10.1016/S0024-3795(01)00494-3zbMath1087.65035OpenAlexW3022873428MaRDI QIDQ1855437

Michiel E. Hochstenbach, Gerard L. G. Sleijpen

Publication date: 5 February 2003

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(01)00494-3

zbMATH Keywords

convergencenumerical examplescorrection equationJacobi-Davidson methodgeneralized eigenproblemRayleigh quotient iterationnonnormal matrixinexact accelerated Newton methodOstrowski's two-sided Rayleigh quotient iterationParlett's alternating Rayleigh quotient iterationpolynomial eigenproblemTwo-sided Lanczos method

Mathematics Subject Classification ID

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

Related Items (15)

A new justification of the Jacobi-Davidson method for large eigenproblems ⋮ Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration ⋮ The nonlinear eigenvalue problem ⋮ Nonlinear Rayleigh functionals ⋮ On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems ⋮ Global convergence of the restarted Lanczos and Jacobi-Davidson methods for symmetric eigenvalue problems ⋮ New iterative methods for generalized singular-value problems ⋮ On the correction equation of the Jacobi-Davidson method ⋮ Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves ⋮ A dynamic thick restarted semi-refined ABLE algorithm for computing a few selected eigentriplets of large nonsymmetric matrices ⋮ The Jacobi-Davidson method ⋮ Inverse Subspace Iteration for Spectral Stochastic Finite Element Methods ⋮ A Jacobi-Davidson type method for the generalized singular value problem ⋮ Rayleigh quotient algorithms for nonsymmetric matrix pencils ⋮ A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem

Cites Work

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• The convergence behavior of Ritz values in the presence of close eigenvalues
• Restarting techniques for the (Jacobi-)Davidson symmetric eigenvalue method
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• Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
• The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• The convergence of Jacobi–Davidson iterations for Hermitian eigenproblems

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