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