Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices

被引：0
作者：
Zhong-Zhi Bai
Fang Chen
Zeng-Qi Wang
机构：
[1] Guizhou Normal University,School of Mathematics and Computer Science
[2] Institute of Computational Mathematics and Scientific/Engineering Computing,State Key Laboratory of Scientific/Engineering Computing
[3] Academy of Mathematics and Systems Science,Key Laboratory of Environmental Mechanics
[4] Chinese Academy of Sciences,Department of Mathematics
[5] Institute of Mechanics,undefined
[6] Chinese Academy of Sciences,undefined
[7] Shanghai Jiaotong University,undefined
来源：
Numerical Algorithms | 2013年 / 62卷
关键词：
Block two-by-two matrices; PMHSS iteration; Block diagonal matrix; Preconditioning; Spectral properties; PDE-constrained optimization; 65F10; 65F50; CR; G1.3;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For a class of block two-by-two systems of linear equations with certain skew-Hamiltonian coefficient matrices, we construct additive block diagonal preconditioning matrices and discuss the eigen-properties of the corresponding preconditioned matrices. The additive block diagonal preconditioners can be employed to accelerate the convergence rates of Krylov subspace iteration methods such as MINRES and GMRES. Numerical experiments show that MINRES preconditioned by the exact and the inexact additive block diagonal preconditioners are effective, robust and scalable solvers for the block two-by-two linear systems arising from the Galerkin finite-element discretizations of a class of distributed control problems.
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页码：655 / 675
页数：20
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