Convergence Analysis of Iterative Solvers in Inexact Rayleigh Quotient Iteration

DOI10.1137/080712908zbMath1201.65060OpenAlexW2053608672MaRDI QIDQ3584136

Fei Xue, Howard C. Elman

Publication date: 19 August 2010

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

Full work available at URL: https://doi.org/10.1137/080712908

zbMATH Keywords

performanceconvergencenumerical experimentsbiharmonic operatorMINRESRayleigh quotient iterationsymmetric positive definite matrixtuned preconditionerbeam bendingharmonic Ritz valuelowest eigenpair

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Positive matrices and their generalizations; cones of matrices (15B48) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items (14)

Convergence proof of the harmonic Ritz pairs of iterative projection methods with restart strategies for symmetric eigenvalue problems ⋮ Efficiently preconditioned inexact Newton methods for large symmetric eigenvalue problems ⋮ Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration ⋮ Low-rank update of preconditioners for the inexact Newton method with SPD Jacobian ⋮ On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems ⋮ On convergence of the inexact Rayleigh quotient iteration with MINRES ⋮ A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems ⋮ Computing the smallest singular triplets of a large matrix ⋮ On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems ⋮ Computing the smallest eigenpairs of the graph Laplacian ⋮ Convergence and preconditioning of inexact inverse subspace iteration for generalized eigenvalue problems ⋮ Acceleration of inverse subspace iteration with Newton's method ⋮ On convergence of iterative projection methods for symmetric eigenvalue problems ⋮ Computing eigenpairs of Hermitian matrices in augmented Krylov subspace produced by Rayleigh quotient iterations

Uses Software

• JDQR
• JDQZ

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