Analysis of acceleration strategies for restarted minimal residual methods

DOI10.1016/S0377-0427(00)00398-8zbMath0968.65016MaRDI QIDQ1591186

Michael Eiermann, Oliver G. Ernst, Olaf Schneider

Publication date: 2 September 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergence accelerationpreconditionerRitz valuesArnoldi methodminimal residual methodsrestartingKrylov-subspace methodsoptimal truncation

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (32)

Any admissible cycle-convergence behavior is possible for restarted GMRES at its initial cycles ⋮ A harmonic restarted Arnoldi algorithm for calculating eigenvalues and determining multiplicity ⋮ Computational aspects of the stochastic finite element method ⋮ A simple strategy for varying the restart parameter in GMRES\((m)\) ⋮ A combination of the fast multipole boundary element method and Krylov subspace recycling solvers ⋮ An adaptive SVD-Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method ⋮ Two-level algebraic domain decomposition preconditioners using Jacobi-Schwarz smoother and adaptive coarse grid corrections ⋮ Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods ⋮ Limited‐memory polynomial methods for large‐scale matrix functions ⋮ Pseudoeigenvector bases and deflated GMRES for highly nonnormal matrices ⋮ Usage of the convergence test of the residual norm in the Tsuno-Nodera version of the GMRES algorithm ⋮ Scalable Convergence Using Two-Level Deflation Preconditioning for the Helmholtz Equation ⋮ A survey of subspace recycling iterative methods ⋮ A refined Arnoldi type method for large scale eigenvalue problems ⋮ Global stability analysis of elastic aircraft in edge-of-the-envelope flow ⋮ On the Spectrum of Deflated Matrices with Applications to the Deflated Shifted Laplace Preconditioner for the Helmholtz Equation ⋮ GMRES algorithms over 35 years ⋮ Multi Space Reduced Basis Preconditioners for Large-Scale Parametrized PDEs ⋮ The behavior of symmetric Krylov subspace methods for solving \(Mx=(M-\gamma I)v\). ⋮ Krylov subspace recycling for sequences of shifted linear systems ⋮ Accelerated GCRO-DR method for solving sequences of systems of linear equations ⋮ Some observations on weighted GMRES ⋮ Iterative solution applied to the Helmholtz equation: complex deflation on unstructured grids ⋮ A proportional-derivative control strategy for restarting the GMRES(\(m\)) algorithm ⋮ GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem ⋮ Efficient optimisation procedure for design problems in fluid mechanics ⋮ Accelerate weighted GMRES by augmenting error approximations ⋮ Convergence conditions for a restarted GMRES method augmented with eigenspaces ⋮ Synthesis of fast and superfast solvers of large systems of linear algebraic equations using control theory methods ⋮ Projections, Deflation, and Multigrid for Nonsymmetric Matrices ⋮ On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES ⋮ The Multilevel Krylov-Multigrid Method for the Helmholtz Equation Preconditioned by the Shifted Laplacian

Uses Software

• eigs
• IRAM

Cites Work

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• Computing interior eigenvalues of large matrices
• Quasi-kernel polynomials and their use in non-Hermitian matrix iterations
• Nested Krylov methods based on GCR
• Restarted GMRES preconditioned by deflation
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
• Geometric aspects of the theory of Krylov subspace methods
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Solution of Sparse Indefinite Systems of Linear Equations
• Adaptively Preconditioned GMRES Algorithms
• Truncation Strategies for Optimal Krylov Subspace Methods
• Analysis of Augmented Krylov Subspace Methods
• Deflated and Augmented Krylov Subspace Techniques
• Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
• Eigenvalue translation based preconditioners for the GMRES(k) method
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• A Restarted GMRES Method Augmented with Eigenvectors
• GMRESR: a family of nested GMRES methods
• On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method
• A Flexible Inner-Outer Preconditioned GMRES Algorithm

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