TY - JOUR
T1 - Improved Relaxed Positive-Definite and Skew-Hermitian Splitting Preconditioners for Saddle Point Problems
AU - Cao , Yang
AU - Ren , Zhiru
AU - Yao , Linquan
JO - Journal of Computational Mathematics
VL - 1
SP - 95
EP - 111
PY - 2018
DA - 2018/08
SN - 37
DO - http://doi.org/10.4208/jcm.1710-m2017-0065
UR - https://global-sci.org/intro/article_detail/jcm/12651.html
KW - Saddle point problems, Preconditioning, RPSS preconditioner, Eigenvalues, Krylov subspace method.
AB - <p style="text-align: justify;">We establish a class of improved relaxed positive-definite and skew-Hermitian splitting
(IRPSS) preconditioners for saddle point problems. These preconditioners are easier to
be implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS)
preconditioner at each step for solving the saddle point problem. We study spectral properties
and the minimal polynomial of the IRPSS preconditioned saddle point matrix. A
theoretical optimal IRPSS preconditioner is also obtained. Numerical results show that
our proposed IRPSS preconditioners are superior to the existing ones in accelerating the
convergence rate of the GMRES method for solving saddle point problems.</p>