Anderson acceleration of the Jacobi iterative method: an efficient alternative to Krylov methods for large, sparse linear systems

DOI10.1016/j.jcp.2015.11.018zbMath1352.65110OpenAlexW2364308289MaRDI QIDQ729311

Phanish Suryanarayana, Phanisri P. Pratapa, John Ernest Pask

Publication date: 20 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2015.11.018

zbMATH Keywords

fixed-point iterationparallel computingHelmholtz equationPoisson equationJacobi methodlinear systems of equationsnonsymmetric matrixAnderson extrapolation

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10)

Related Items (16)

Large scale \textit{ab-initio} simulations of dislocations ⋮ Least squares methods in Krylov subspaces ⋮ Anderson acceleration based on the \(\mathcal{H}^{- s}\) Sobolev norm for contractive and noncontractive fixed-point operators ⋮ Unifying relations between iterative linear equation solvers and explicit Euler approximations for associated parabolic regularized equations ⋮ Alternating Anderson-Richardson method: an efficient alternative to preconditioned Krylov methods for large, sparse linear systems ⋮ Projection Improved SPAI Preconditioner for FGMRES ⋮ Anderson acceleration method of finding steady-state particle size distribution for a wide class of aggregation-fragmentation models ⋮ SQDFT: spectral quadrature method for large-scale parallel \(\mathcal{O}(N)\) Kohn-Sham calculations at high temperature ⋮ Nonmonotone globalization for Anderson acceleration via adaptive regularization ⋮ An iterative method for 2D inverse scattering problems by alternating reconstruction of medium properties and wavefields: theory and application to the inversion of elastic waveforms ⋮ Acceleration of the scheduled relaxation Jacobi method: promising strategies for solving large, sparse linear systems ⋮ Uzawa-Type and Augmented Lagrangian Methods for Double Saddle Point Systems ⋮ Efficient relaxed-Jacobi smoothers for multigrid on parallel computers ⋮ Iterative preconditioned methods in Krylov spaces: trends of the 21st century ⋮ A new Jacobi-type iteration method for solving M-matrix or nonnegative linear systems ⋮ Cyclic density functional theory: a route to the first principles simulation of bending in nanostructures

Cites Work

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• An analysis for the DIIS acceleration method used in quantum chemistry calculations
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• Acceleration of the Jacobi iterative method by factors exceeding 100 using scheduled relaxation
• Non-periodic finite-element formulation of Kohn-Sham density functional theory
• A characterization of the behavior of the Anderson acceleration on linear problems
• Coarse-graining Kohn-Sham density functional theory
• Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory
• Two classes of multisecant methods for nonlinear acceleration
• Anderson Acceleration for Fixed-Point Iterations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Nonlinear acceleration of coupled fluid–structure transient thermal problems by Anderson mixing
• An Iterative Least-Square Method Suitable for Solving Large Sparse Matrices
• Iterative Procedures for Nonlinear Integral Equations
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