 A doubly stochastic block Gauss–Seidel algorithm for solving linear equationsKui Du and Xiao-Hui Sun Applied Mathematics and Computation, 2021, vol. 408, issue C Abstract: We propose a doubly stochastic block Gauss–Seidel algorithm for solving linear systems of equations. By varying the row partition parameter and the column partition parameter for the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized coordinate descent algorithm, and the doubly stochastic Gauss–Seidel algorithm. For arbitrary (consistent or inconsistent, full column rank or rank-deficient) linear systems, we prove the exponential convergence of the norm of the expected error via exact formulas. We also prove the exponential convergence of the expected norm of the error for consistent linear systems, and the exponential convergence of the expected norm of the residual for arbitrary linear systems. Numerical experiments for linear systems with synthetic and real-world coefficient matrices are given to demonstrate the efficiency of our algorithm. Keywords: Randomized Kaczmarz; Randomized coordinate descent; Doubly stochastic Gauss–Seidel; Doubly stochastic block Gauss–Seidel; Exponential convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004628 DOI: 10.1016/j.amc.2021.126373 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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