GMRES Convergence for Perturbed Coefficient Matrices, with Application to Approximate Deflation Preconditioning

DOI10.1137/120884328zbMath1314.65051OpenAlexW2041660628MaRDI QIDQ2866224

Josef Sifuentes, Ronald B. Morgan, Mark Embree

Publication date: 13 December 2013

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

Full work available at URL: https://semanticscholar.org/paper/2e0af2f5836c0a7dd075999c7d59c0c9cbb80702

zbMATH Keywords

convergenceresolventperturbation theoryRitz vectorgeneralized minimal residual (GMRES) methoddeflation preconditioning

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Related Items (14)

Analysis on block diagonal and triangular preconditioners for a PML system of an electromagnetic scattering problem ⋮ Pseudoeigenvector bases and deflated GMRES for highly nonnormal matrices ⋮ Krylov solvability under perturbations of abstract inverse linear problems ⋮ A survey of subspace recycling iterative methods ⋮ Deflation for the Off-Diagonal Block in Symmetric Saddle Point Systems ⋮ A Class of Approximate Inverse Preconditioners Based on Krylov-Subspace Methods for Large-Scale Nonconvex Optimization ⋮ On the Spectrum of Deflated Matrices with Applications to the Deflated Shifted Laplace Preconditioner for the Helmholtz Equation ⋮ GMRES algorithms over 35 years ⋮ A flexible and adaptive simpler block GMRES with deflated restarting for linear systems with multiple right-hand sides ⋮ Motivations and realizations of Krylov subspace methods for large sparse linear systems ⋮ Two-Grid and Multiple-Grid Arnoldi for Eigenvalues ⋮ Projections, Deflation, and Multigrid for Nonsymmetric Matrices ⋮ A GMRES Convergence Analysis for Localized Invariant Subspace Ill-Conditioning ⋮ On uniform connectivity of algebraic matrix sets

Uses Software

• ARPACK
• Eigtool

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