Gradient Flow Approach to Geometric Convergence Analysis of Preconditioned Eigensolvers

DOI10.1137/080727567zbMath1191.49039arXiv0801.3099OpenAlexW2139039544WikidataQ59695797 ScholiaQ59695797MaRDI QIDQ3561175

Klaus Neymeyr, Andrew V. Knyazev

Publication date: 25 May 2010

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

Full work available at URL: https://arxiv.org/abs/0801.3099

zbMATH Keywords

eigenvalueeigenvectorpreconditioningiterative methodcontinuation methodRayleigh quotientpreconditionerconvergence theoryspectral equivalencegradient iteration

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical optimization and variational techniques (65K10) Numerical methods based on nonlinear programming (49M37) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items

Convergence theory for preconditioned eigenvalue solvers in a nutshell ⋮ On the approximation of electronic wavefunctions by anisotropic Gauss and Gauss-Hermite functions ⋮ Hybrid eigensolvers for nuclear configuration interaction calculations ⋮ Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization ⋮ An indefinite variant of LOBPCG for definite matrix pencils ⋮ The preconditioned inverse iteration for hierarchical matrices ⋮ On convergence of iterative projection methods for symmetric eigenvalue problems ⋮ Preconditioned gradient iterations for the eigenproblem of definite matrix pairs ⋮ Cluster robust estimates for block gradient-type eigensolvers