TY - JOUR
T1 - A Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems
AU - Shao , Xinhui
AU - Li , Chen
AU - Zhang , Tie
AU - Li , Changjun
JO - Journal of Computational Mathematics
VL - 4
SP - 579
EP - 590
PY - 2018
DA - 2018/06
SN - 36
DO - http://doi.org/10.4208/jcm.1702-m2016-0665
UR - https://global-sci.org/intro/article_detail/jcm/12306.html
KW - Preconditioner, Inexact Uzawa method, Saddle point problems, Indefiniteness, Convergence.
AB - <p style="text-align: justify;">The preconditioner for parameterized inexact Uzawa methods has been used to solve
some indefinite saddle point problems. Firstly, we modify the preconditioner by making it
more generalized, then we use theoretical analyses to show that the iteration method converges
under certain conditions. Moreover, we discuss the optimal parameter and matrices
based on these conditions. Finally, we propose two improved methods. Numerical experiments
are provided to show the effectiveness of the modified preconditioner. All methods
have fantastic convergence rates by choosing the optimal parameter and matrices.</p>