Year: 2022
Author: Ai-Li Yang, Xue-Qi Chen
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 4 : pp. 874–890
Abstract
A greedy Gauss-Seidel based on the greedy Kaczmarz algorithm and aimed to find approximations of the solution $A^†b$ of systems of linear algebraic equations with a full column-rank coefficient matrix $A$ is proposed. Developing this approach, we introduce a partially greedy randomized extended Gauss-Seidel method for finding approximate least-norm least-squares solutions of column-rank deficient linear systems. The convergence of the methods is studied. Numerical experiments show that the proposed methods are robust and efficient.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.300921.170422
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 4 : pp. 874–890
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Systems of linear equations least-squares solution randomized extended Gauss-Seidel method convergence.