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 - <p style="text-align: justify;">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.</p>