TY - JOUR
T1 - Regularized DPSS Preconditioners for Singular Saddle Point Problems
AU - Qian , Yong
AU - Zhang , Guofeng
AU - Liang , Zhaozheng
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 986
EP - 1006
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0123
UR - https://global-sci.org/intro/article_detail/nmtma/16963.html
KW - Singular saddle point problem, DPSS preconditioner, preconditioning, semi-convergence.
AB - <p style="text-align: justify;">Recently, Cao proposed a regularized deteriorated positive and skew-Hermitian splitting (RDPSS) preconditioner for the non-Hermitian nonsingular saddle point problem. In this paper, we consider applying RDPSS preconditioner to
solve the singular saddle point problem. Moreover, we propose a two-parameter
accelerated variant of the RDPSS (ARDPSS) preconditioner to further improve its
efficiency. Theoretical analysis proves that the RDPSS and ARDPSS methods are
semi-convergent unconditionally. Some spectral properties of the corresponding preconditioned matrices are analyzed. Numerical experiments indicate that better performance can be achieved when applying the ARDPSS preconditioner to accelerate
the GMRES method for solving the singular saddle point problem.</p>