TY - JOUR T1 - SOR-Like Methods with Optimization Model for Augmented Linear Systems JO - East Asian Journal on Applied Mathematics VL - 1 SP - 101 EP - 115 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.010916.261116a UR - https://global-sci.org/intro/article_detail/eajam/10737.html KW - SOR-like method, optimization, augmented linear systems, convergence. AB -
There has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001)71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter ω by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.