A geometric theory for preconditioned inverse iteration IV: On the fastest convergence cases

DOI10.1016/j.laa.2005.06.022zbMath1088.65034OpenAlexW2079227511WikidataQ56335056 ScholiaQ56335056MaRDI QIDQ2368743

Klaus Neymeyr

Publication date: 28 April 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.06.022

zbMATH Keywords

Rayleigh quotientConvergenceInverse iterationMultigridPreconditionerGradient iterationElliptic partial differential operatorSymmetric eigenvalue problem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Boundary value problems for second-order elliptic equations (35J25) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (4)

Cluster robustness of preconditioned gradient subspace iteration eigensolvers ⋮ A new justification of the Jacobi-Davidson method for large eigenproblems ⋮ On preconditioned eigensolvers and invert-Lanczos processes ⋮ Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

Uses Software

• JDQZ
• lobpcg.m

Cites Work

• A subspace preconditioning algorithm for eigenvector/eigenvalue computation
• Iteration methods in eigenvalue problems
• Minimization of the computational labor in determining the first eigenvalues of differential operators
• 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. I: Extrema of Rayleigh quotient
• A geometric theory for preconditioned inverse iteration. II: Convergence estimates
• A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems
• A geometric theory for preconditioned inverse iteration applied to a subspace
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
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