Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems
Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems
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DOI：
10.1093/imanum/drs001
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发表时间：
2013
影响因子：
2.1
通讯作者：
Z. Bai;M. Benzi;Fang Chen;Zeng-Qi Wang
中科院分区：
文献类型：
--
作者：
Z. Bai;M. Benzi;Fang Chen;Zeng-Qi Wang
本文构造了一种预处理的修正Hermitian和斜Hermitian分裂（PMHSS）迭代格式，用于求解一类分布控制问题的Galerkin有限元离散化所产生的块二乘二线性方程组.建立了这类PMHSS迭代法的收敛性理论，分析了PMHSS预条件矩阵的谱性质。数值实验表明，PMHSS预处理器可以相当有竞争力的预处理Krylov子空间迭代方法，如GMRES。
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.