Volume 12, Issue 4
A Partially Greedy Randomized Extended Gauss-Seidel Method for Solving Large Linear Systems

East Asian J. Appl. Math., 12 (2022), pp. 874-890.

Published online: 2022-08

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• 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.

• Keywords

Systems of linear equations, least-squares solution, randomized extended Gauss-Seidel method, convergence.

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@Article{EAJAM-12-874, author = {Ai-Li and Yang and and 24361 and and Ai-Li Yang and Xue-Qi and Chen and and 24362 and and Xue-Qi Chen}, title = {A Partially Greedy Randomized Extended Gauss-Seidel Method for Solving Large Linear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.300921.170422}, url = {http://global-sci.org/intro/article_detail/eajam/20888.html} }
TY - JOUR T1 - A Partially Greedy Randomized Extended Gauss-Seidel Method for Solving Large Linear Systems AU - Yang , Ai-Li AU - Chen , Xue-Qi JO - East Asian Journal on Applied Mathematics VL - 4 SP - 874 EP - 890 PY - 2022 DA - 2022/08 SN - 12 DO - http://doi.org/10.4208/eajam.300921.170422 UR - https://global-sci.org/intro/article_detail/eajam/20888.html KW - Systems of linear equations, least-squares solution, randomized extended Gauss-Seidel method, convergence. AB -

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.

Ai-Li Yang & Xue-Qi Chen. (2022). A Partially Greedy Randomized Extended Gauss-Seidel Method for Solving Large Linear Systems. East Asian Journal on Applied Mathematics. 12 (4). 874-890. doi:10.4208/eajam.300921.170422
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