Modified Bernoulli iteration methods for quadratic matrix equation

	Modified Bernoulli iteration methods for quadratic matrix equation
	Bai, Zhong-Zhi; Gao, Yong-Hua
	2007-09-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	25 期号:5 页码:498-511
摘要	We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX(2) + BX + C = 0, where A, B and C are square matrices. This method is motivated from the Gauss-Seidel iteration for solving linear systems and the Sherman-Morrison-Woodbury formula for updating matrices. Under suitable conditions, we prove the local linear convergence of the new method. An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm. In addition, we also describe and analyze the block version of the modified Bernoulli iteration method.
关键词	quadratic matrix equation quadratic eigenvalue problem solvent Bernoulli's iteration Newton's method local convergence
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000249440300002
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4989
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Gao, Yong-Hua. Modified Bernoulli iteration methods for quadratic matrix equation[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2007,25(5):498-511.
APA	Bai, Zhong-Zhi,&Gao, Yong-Hua.(2007).Modified Bernoulli iteration methods for quadratic matrix equation.JOURNAL OF COMPUTATIONAL MATHEMATICS,25(5),498-511.
MLA	Bai, Zhong-Zhi,et al."Modified Bernoulli iteration methods for quadratic matrix equation".JOURNAL OF COMPUTATIONAL MATHEMATICS 25.5(2007):498-511.