Sharp Ritz value estimates for restarted Krylov subspace iterations

zbMath1392.65103MaRDI QIDQ1744300

Ming Zhou, Klaus Neymeyr

Publication date: 23 April 2018

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2011-2020/vol46/abstract.php?vol=46&pages=424-446

zbMATH Keywords

Rayleigh quotientmultigridRayleigh-Ritz procedureelliptic eigenvalue problempolynomial interpolationKrylov subspace

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (1)

Sharp Majorization-Type Cluster Robust Bounds for Block Filters and Eigensolvers

Uses Software

• JDQR
• JDQZ

Cites Work

• On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem
• On preconditioned eigensolvers and invert-Lanczos processes
• Preconditioning eigensolvers -- an Oxymoron?
• Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method
• A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems
• Convergence theory for preconditioned eigenvalue solvers in a nutshell
• The block preconditioned steepest descent iteration for elliptic operator eigenvalue problems
• Iterative minimization of the Rayleigh quotient by block steepest descent iterations
• Convergence Analysis of Gradient Iterations for the Symmetric Eigenvalue Problem
• Convergence Analysis of Restarted Krylov Subspace Eigensolvers
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• A Generalized Lanczos Scheme
• Templates for the Solution of Algebraic Eigenvalue Problems
• A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration
• Estimates for Some Computational Techniques in Linear Algebra
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