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.