Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems

被引：206

作者：

Bai, Zhong-Zhi ^{[1
]}

Benzi, Michele ^{[2
]}

Chen, Fang ^{[3
]}

Wang, Zeng-Qi ^{[4
]}

机构：

[1] Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 USA

[3] Chinese Acad Sci, Key Lab Environm Mech, Inst Mech, Beijing 100190, Peoples R China

[4] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2013年 / 33卷 / 01期

关键词：

block two-by-two matrices; PMHSS iteration; preconditioning; spectral properties; PDE-constrained optimization; KKT systems; HERMITIAN SPLITTING METHODS;

D O I：

10.1093/imanum/drs001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct a preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration scheme for solving and preconditioning a class of block two-by-two linear systems arising from the Galerkin finite element discretizations of a class of distributed control problems. The convergence theory of this class of PMHSS iteration methods is established and the spectral properties of the PMHSS-preconditioned matrix are analysed. Numerical experiments show that the PMHSS preconditioners can be quite competitive when used to precondition Krylov subspace iteration methods such as GMRES.

引用

页码：343 / 369

页数：27