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	Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations
	Bai, Zhong-Zhi ; Guo, Xiao-Xia ; Xu, Shu-Fang
	2006
关键词	non-symmetric algebraic Riccati equation minimal non-negative solution M-matrix alternately linearized iteration monotone convergence HERMITIAN SPLITTING METHODS H-INFINITY OPTIMIZATION SCHUR METHOD MATRIX SYSTEMS SUBSPACES ALGORITHM DESIGN
英文摘要	For the non-symmetric algebraic Riccati equations, we establish a class of alternately linearized implicit (ALI) iteration methods for computing its minimal non-negative solutions by technical combination of alternate splitting and successive approximating of the algebraic Riccati operators. These methods include one iteration parameter, and suitable choices of this parameter may result in fast convergent iteration methods. Under suitable conditions, we prove the monotone convergence and estimate the asymptotic convergence factor of the ALI iteration matrix sequences. Numerical experiments show that the ALI iteration methods are feasible and effective, and can outperform the Newton iteration method and the fixed-point iteration methods. Besides, we further generalize the known fixed-point iterations, obtaining an extensive class of relaxed splitting iteration methods for solving the non-symmetric algebraic Riccati equations. Copyright (C) 2006 John Wiley & Sons, Ltd.; Mathematics, Applied; Mathematics; SCI(E); 0; ARTICLE; 8; 655-674; 13
语种	英语
出处	SCI
出版者	numerical linear algebra with applications
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/251540]
专题	数学科学学院
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Guo, Xiao-Xia,Xu, Shu-Fang. Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations. 2006-01-01.

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