A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems

DOI10.1016/j.cam.2008.10.071zbMath1186.65044OpenAlexW2075516171MaRDI QIDQ1044859

Qiang Ye, Patrick Quillen

Publication date: 15 December 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.10.071

zbMATH Keywords

algorithmnumerical examplespreconditioningArnoldi algorithmsymmetric eigenvalue problemclustered eigenvaluesblock Krylov subspace methodincomplete factorizations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Preconditioners for iterative methods (65F08)

Related Items (11)

Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods ⋮ Locally optimal and heavy ball GMRES methods ⋮ Updating component reduction bases of static and vibration modes using preconditioned iterative techniques ⋮ Generalized Preconditioned Locally Harmonic Residual Method for Non-Hermitian Eigenproblems ⋮ Deflation by restriction for the inverse-free preconditioned Krylov subspace method ⋮ Preconditioned gradient iterations for the eigenproblem of definite matrix pairs ⋮ A simple extrapolation method for clustered eigenvalues ⋮ A method for computing a few eigenpairs of large generalized eigenvalue problems ⋮ On generalizing trace minimization principles ⋮ Triangularized orthogonalization-free method for solving extreme eigenvalue problems ⋮ A Block Arnoldi Method for the SPN Equations

Uses Software

• EIGIFP
• JDQR
• JDCG
• ABLE
• lobpcg.m

Cites Work

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• Inexact inverse iteration for generalized eigenvalue problems
• A geometric theory for preconditioned inverse iteration. I: Extrema of Rayleigh quotient
• A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems
• Preconditioning techniques for large linear systems: A survey
• An adaptive block Lanczos algorithm
• Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
• IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
• An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
• Lanczos Algorithms for Large Symmetric Eigenvalue Computations
• Combination of Jacobi–Davidson and conjugate gradients for the partial symmetric eigenproblem
• Algorithm 845
• A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods

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