A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration

DOI10.1137/11084488XzbMath1262.65051arXiv1108.2365MaRDI QIDQ4907156

Klaus Neymeyr

Publication date: 4 March 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2365

zbMATH Keywords

Rayleigh quotientgeneralized eigenvalue problemsteepest descentpreconditionersymmetric positive definite matricesfirst eigenvaluegradient iteration

Mathematics Subject Classification ID

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

Related Items (11)

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 ⋮ Hybrid eigensolvers for nuclear configuration interaction calculations ⋮ 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 ⋮ Convergence theory of exact interpolation scheme for computing several eigenvectors ⋮ 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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