Stochastic iterative projection methods for large linear systems

DOI10.1515/MCMA.2010.020zbMath1206.65135MaRDI QIDQ3068189

Nadja Loshchina, K. K. Sabel'fel'd

Publication date: 13 January 2011

Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical examplesparallel computationfinite-differencePoisson equationsystems of linear inequalitiesrandom projectionsrandom walk algorithmKaczmarz's methodoverdetermined systemsrandom sparsificationJohnson-Lindenstrauss theoremMarkov chain based Neumann-Ulam schemerandom row-action

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (9)

Corrigendum to: ``A stochastic spectral projection method for solving PDEs in domains composed by overlapping discs, spheres, and half-spaces ⋮ Vector Monte Carlo stochastic matrix-based algorithms for large linear systems ⋮ Territorial design optimization for business sales plan ⋮ Randomized Monte Carlo algorithms for matrix iterations and solving large systems of linear equations ⋮ Stochastic projection methods and applications to some nonlinear inverse problems of phase retrieving ⋮ Stochastic boundary methods of fundamental solutions for solving PDEs ⋮ Unnamed Item ⋮ A new randomized vector algorithm for iterative solution of large linear systems ⋮ Global random walk on grid algorithm for solving Navier-Stokes and Burgers equations

Cites Work

• A fast randomized algorithm for the approximation of matrices
• A randomized Kaczmarz algorithm with exponential convergence
• Projection method for solving a singular system of linear equations and its applications
• Sparsified Randomization Algorithms for large systems of linear equations and a new version of the Random Walk on Boundary method
• The Fast Johnson–Lindenstrauss Transform and Approximate Nearest Neighbors
• Fast monte-carlo algorithms for finding low-rank approximations
• Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication

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