Greedy and randomized versions of the multiplicative Schwarz method

DOI10.1016/j.laa.2012.04.052zbMath1251.65048OpenAlexW2074130980MaRDI QIDQ445816

Peter Oswald, Michael Griebel

Publication date: 27 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.04.052

zbMATH Keywords

numerical resultsfinite elementsPoisson equationexponential convergencemultiplicative Schwarz methodsToeplitz systemgreedy and randomized ordersHilbert space splittingslarge linear systemSouthwell methodsubspace corrections

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (19)

Stochastic subspace correction in Hilbert space ⋮ Convergence of a randomized Douglas-Rachford method for linear system ⋮ Fault Resilient Domain Decomposition Preconditioner for PDEs ⋮ Adaptively sketched Bregman projection methods for linear systems ⋮ Optimal scaling parameters for sparse grid discretizations ⋮ On the algebraic construction of sparse multilevel approximations of elliptic tensor product problems ⋮ On the convergence of randomized and greedy relaxation schemes for solving nonsingular linear systems of equations ⋮ On multi-step randomized extended Kaczmarz method for solving large sparse inconsistent linear systems ⋮ Triangular truncation and its extremal matrices ⋮ On convergence rates of Kaczmarz-type methods with different selection rules of working rows ⋮ Subspace correction methods in algebraic multi-level frames ⋮ Randomized Douglas–Rachford Methods for Linear Systems: Improved Accuracy and Efficiency ⋮ A Sampling Kaczmarz--Motzkin Algorithm for Linear Feasibility ⋮ On convergence rate of the randomized Gauss-Seidel method ⋮ Schwarz iterative methods: infinite space splittings ⋮ Stochastic subspace correction methods and fault tolerance ⋮ Randomized and fault-tolerant method of subspace corrections ⋮ On Adaptive Sketch-and-Project for Solving Linear Systems ⋮ Convergence analysis for Kaczmarz-type methods in a Hilbert space framework

Uses Software

• AFACx

Cites Work

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