A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation

doi:10.1007/s00211-005-0673-7

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	A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation
	Guo, XX ; Lin, WW ; Xu, SF
	2006-05-01
发表期刊	NUMERISCHE MATHEMATIK
ISSN	0029-599X
卷号	103 期号:3 页码:393-412
摘要	In this paper, we propose a structure-preserving doubling algorithm (SDA) for the computation of the minimal nonnegative solution to the nonsymmetric algebraic Riccati equation (NARE), based on the techniques developed for the symmetric cases. This method allows the simultaneous approximation to the minimal nonnegative solutions of the NARE and its dual equation, requiring only the solutions to two linear systems and several matrix multiplications per iteration. Similar to Newton's method and the fixed-point iteration methods for solving NAREs, we also establish global convergence for SDA under suitable conditions, using only elementary matrix theory. We show that sequences of matrices generated by SDA are monotonically increasing and quadratically convergent to the minimal nonnegative solutions of the NARE and its dual equation. Numerical experiments show that the SDA algorithm is feasible and effective, and outperforms Newton's iteration and the fixed-point iteration methods.
关键词	nonsymmetric algebraic Riccati equation minimal nonnegative solution structure-preserving doubling algorithm
DOI	10.1007/s00211-005-0673-7
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000237189800003
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2498
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, XX
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 100080, Peoples R China 2.Natl Tsing Hua Univ, Dept Math, Hsinchu 300, Taiwan 3.Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Guo, XX,Lin, WW,Xu, SF. A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation[J]. NUMERISCHE MATHEMATIK,2006,103(3):393-412.
APA	Guo, XX,Lin, WW,&Xu, SF.(2006).A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation.NUMERISCHE MATHEMATIK,103(3),393-412.
MLA	Guo, XX,et al."A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation".NUMERISCHE MATHEMATIK 103.3(2006):393-412.