Efficient Preconditioned Inner Solves For Inexact Rayleigh Quotient Iteration And Their Connections To The Single-Vector Jacobi–Davidson Method

DOI10.1137/100807922zbMath1238.65028OpenAlexW1971837295WikidataQ115156439 ScholiaQ115156439MaRDI QIDQ3112404

Fei Xue, Daniel B. Szyld

Publication date: 16 January 2012

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

Full work available at URL: https://doi.org/10.1137/100807922

zbMATH Keywords

convergencegeneralized eigenvalue problemJacobi-Davidson methodRayleigh quotient iterationtuned preconditionerKrylov subspace inner solves

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items (14)

GMRES convergence bounds for eigenvalue problems ⋮ 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 ⋮ Disguised and new quasi-Newton methods for nonlinear eigenvalue problems ⋮ Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ On convergence of the inexact Rayleigh quotient iteration with MINRES ⋮ On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems ⋮ On expansion of search subspaces for large non-Hermitian eigenproblems ⋮ Broyden's Method for Nonlinear Eigenproblems ⋮ On convergence of iterative projection methods for symmetric eigenvalue problems ⋮ Computing eigenpairs of Hermitian matrices in augmented Krylov subspace produced by Rayleigh quotient iterations ⋮ Tuned preconditioners for the eigensolution of large SPD matrices arising in engineering problems ⋮ A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible \(M\)-matrix

Uses Software

• JDQR
• IFISS
• JDQZ

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