On contraction factors of Hermitian and skew-Hermitian splitting iteration method for generalized saddle point problems

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	On contraction factors of Hermitian and skew-Hermitian splitting iteration method for generalized saddle point problems
	Chen F(陈芳); Jiang YL(蒋耀林)
刊名	应用数学与计算数学学报/COMMUN．APPL．MATH．COMPUT
	2012-03-15
卷号	26 期号:1 页码:28-34
关键词	收缩因子加权2-范数 2-范数广义鞍点问题 HSS迭代方法 contraction factor weighted 2-norm 2-norm generalized saddle point problem Hermitian and skew-Hermitian splitting (HSS) iteration method
ISSN号	1006-6330
其他题名	关于广义鞍点问题的HSS迭代方法的收缩因子
通讯作者	陈芳
产权排序	西安交通大学理学院;中国科学院力学研究所环境力学重点实验室
合作状况	国内
中文摘要	The Hermitian and skew-Hermitian splitting(HSS) iteration method was presented and studied by Bai,et al.for solving non-Hermitian positive definite linear systems(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems.SIAM J.Matrix Anal.Appl,2003,24:603-626). In this paper,contraction factors of the HSS iteration method in terms of the weighted 2-norm and the 2-norm are given,respectively, for the generalized saddle point problems. These contraction factors rather than the spectral radius of the iteration matrix essentially control the actual convergent speed of the HSS iteration method in practical computations．According to the analyses the contraction fator of the HSS iteration method for the generalized saddle point problem is one in the weighted 2-norm ．However．it nay be greater than or equal to one in the 2-norm and less than one in other suitable norms．Finally, numerical examples are used to examine the correctness of the theoretical results．
英文摘要	白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂(HSS)迭代方法(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methodsfor non-Hermitian positive definite linear systems.SIAM J.Matrix Anal.Appl.,2003,24:603-626).本文精确地估计了用HSS迭代方法求解广义鞍点问题时在加权2-范数和2-范数下的收缩因子.在实际的计算中,正是这些收缩因子而不是迭代矩阵的谱半径,本质上控制着HSS迭代方法的实际收敛速度.根据文中的分析,求解广义鞍点问题的HSS迭代方法的收缩因子在加权2-范数下等于1,在2-范数下它会大于等于1,而在某种适当选取的范数之下,它则会小于1.最后,用数值算例说明了理论结果的正确性.
学科主题	计算流体力学
资助信息	Project supported by the State Key Laboratory of Scientific/ Engineering Computing,Chinese Academy of Sciences; the International Science and Technology Cooperation Program of China(2010DFA14700); the National Natural Science Foundation of China(11071192)
原文出处	http://epub.cnki.net/kns/detail/detail.aspx?FileName=YONG201201006&DbName=CJFQ2012
语种	英语
公开日期	2013-01-16
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/46458]
专题	力学研究所_流固耦合系统力学重点实验室(2012-)
推荐引用方式 GB/T 7714	Chen F,Jiang YL. On contraction factors of Hermitian and skew-Hermitian splitting iteration method for generalized saddle point problems[J]. 应用数学与计算数学学报/COMMUN．APPL．MATH．COMPUT,2012,26(1):28-34.
APA	陈芳,&蒋耀林.(2012).On contraction factors of Hermitian and skew-Hermitian splitting iteration method for generalized saddle point problems.应用数学与计算数学学报/COMMUN．APPL．MATH．COMPUT,26(1),28-34.
MLA	陈芳,et al."On contraction factors of Hermitian and skew-Hermitian splitting iteration method for generalized saddle point problems".应用数学与计算数学学报/COMMUN．APPL．MATH．COMPUT 26.1(2012):28-34.