Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems

doi:10.1515/cmam-2017-0006

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	Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems
	Huang, Na 1; Ma, Chang-Feng 2,3; Zou, Jun 4
	2018-04-01
发表期刊	COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
ISSN	1609-4840
卷号	18 期号:2 页码:237-256
摘要	We first derive some explicit bounds on the spectra of generalized non-symmetric singular or non-singular saddle point matrices. Then we propose two new nonsingular preconditioners for solving generalized singular saddle point problems, and show that GMRES determines a solution without breakdown when applied to the resulting preconditioned systems with any initial guess. Furthermore, the detailed spectral properties of the preconditioned systems are analyzed. The nonsingular preconditioners are also applied to solve the singular finite element saddle point systems arising from the discretization of the Stokes problems to test their performance.
关键词	Singular Saddle Point Problems Preconditioners Spectral Estimates
DOI	10.1515/cmam-2017-0006
语种	英语
资助项目	National Postdoctoral Program for Innovative Talents[BX201600182] ; China Postdoctoral Science Foundation[2016M600141] ; CUHK ; National Natural Science Foundation of China[11071041] ; Fujian Natural Science Foundation[2016J01005] ; Hong Kong RGC grant[14306814] ; National Natural Science Foundation (NSFC)/Research Grants Council (RGC) Joint Research Scheme[N_CUHK437/16]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000428185200006
出版者	WALTER DE GRUYTER GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30092
专题	中国科学院数学与系统科学研究院
通讯作者	Zou, Jun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Fujian, Peoples R China 3.Fujian Normal Univ, FJKLMAA, Fuzhou 350007, Fujian, Peoples R China 4.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Huang, Na,Ma, Chang-Feng,Zou, Jun. Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems[J]. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS,2018,18(2):237-256.
APA	Huang, Na,Ma, Chang-Feng,&Zou, Jun.(2018).Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems.COMPUTATIONAL METHODS IN APPLIED MATHEMATICS,18(2),237-256.
MLA	Huang, Na,et al."Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems".COMPUTATIONAL METHODS IN APPLIED MATHEMATICS 18.2(2018):237-256.