A doubly stochastic block Gauss-Seidel algorithm for solving linear equations

12/31/2019

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by   Kui Du, et al.

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We propose a simple doubly stochastic block Gauss-Seidel algorithm for solving linear systems of equations. By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized Gauss-Seidel algorithm, and the doubly stochastic Gauss-Seidel algorithm. We prove the exponential convergence of the norm of the expected error for general linear systems (consistent or inconsistent, full rank or rank deficient). In addition, we also show the exponential convergence of the expected norm of the error for full-column rank consistent linear systems.