Convergence Analysis of Gradient Iterations for the Symmetric Eigenvalue Problem

DOI10.1137/100784928zbMath1230.65049OpenAlexW1974907720MaRDI QIDQ3094395

Ming Zhou, Klaus Neymeyr, Evgueni E. Ovtchinnikov

Publication date: 25 October 2011

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

Full work available at URL: https://doi.org/10.1137/100784928

zbMATH Keywords

convergenceRayleigh quotientpreconditionerelliptic eigenvalue problemKrylov subspacesRitz vectorgradient iterationRitz valuegeneralized matrix eigenvalue problemsteepest descent/ascent

Mathematics Subject Classification ID

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

Related Items (9)

Convergence theory for preconditioned eigenvalue solvers in a nutshell ⋮ Convergence Analysis of Restarted Krylov Subspace Eigensolvers ⋮ Iterative minimization of the Rayleigh quotient by block steepest descent iterations ⋮ An indefinite variant of LOBPCG for definite matrix pencils ⋮ Convergence rates of individual Ritz values in block preconditioned gradient-type eigensolvers ⋮ Sharp Ritz value estimates for restarted Krylov subspace iterations ⋮ 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

Uses Software

• JDQR
• JDQZ

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