Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems

doi:10.1016/j.camwa.2017.07.018

	Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems
	Huang, Na 1,2; Ma, Chang-Feng 2
	2017-11-15
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	74 期号:10 页码:2423-2437
摘要	By using the Galerkin finite element method, the distributed control problems can be discretized into a saddle point problem with a coefficient matrix of block three-by-three, which can be reduced to a linear system with lower order. We first introduce a class of inexact block diagonal preconditioners and estimate the lower and upper bounds of positive and negative eigenvalues of the preconditioned matrices, respectively. Based on the Cholesky decomposition of the known matrices, we also analyze a lower triangular preconditioner to accelerate the minimal residual method for the reduced linear system and discuss its real and complex eigenvalues respectively. Moreover, these bounds do not rely on the regularization parameter and the eigenvalues of the matrices in the discrete system. Numerical experiments are also presented to demonstrate the effectiveness and robustness of the two new preconditioners. (C) 2017 Elsevier Ltd. All rights reserved.
关键词	PDE-constrained optimization Saddle point matrices Preconditioner Cholesky decomposition Spectral bound
DOI	10.1016/j.camwa.2017.07.018
语种	英语
资助项目	National Postdoctoral Program for Innovative Talents[BX201600182] ; China Postdoctoral Science Foundation[2016M600141] ; National Natural Science Foundation of China[11071041] ; Fujian Natural Science Foundation[02016J01005] ; Fujian Natural Science Foundation[2015J01578]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000415908400015
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/123
专题	计算数学与科学工程计算研究所
通讯作者	Ma, Chang-Feng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China 2.Fujian Normal Univ, Coll Math & Informat, Fujian Key Lab Math Anal & Applicat, Fuzhou 350117, Fujian, Peoples R China
推荐引用方式 GB/T 7714	Huang, Na,Ma, Chang-Feng. Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,74(10):2423-2437.
APA	Huang, Na,&Ma, Chang-Feng.(2017).Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems.COMPUTERS & MATHEMATICS WITH APPLICATIONS,74(10),2423-2437.
MLA	Huang, Na,et al."Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems".COMPUTERS & MATHEMATICS WITH APPLICATIONS 74.10(2017):2423-2437.

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