East Asian J. Appl. Math., 12 (2022), pp. 874-890.
Published online: 2022-08
Cited by
- BibTex
- RIS
- TXT
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} }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.