New Alternately Linearized Implicit Iteration for M-matrix Algebraic Riccati Equations  

作　　者：Jinrui Guan Linzhang Lu 

机构地区：[1]Department of Mathematics,Taiyuan Normal University,Shanxi 030619,P.R.China [2]School of Mathematics and Computer Science,Guizhou Normal University,Guizhou 550001,P.R.China.

出　　处：《Journal of Mathematical Study》2017年第1期54-64,共11页数学研究（英文）

基　　金：The authors would like to thank the anonymous referees and Prof.Ren-Cang Li for their kindly suggestions and comments,which greatly improved the original manuscript of this paper.This work was supported in part by National Natural Science Foundation of China(11671105);Natural Science Foundation of China(11401424).

摘　　要：Research on the theories and the efficient numerical methods of M-matrix algebraic Riccati equation(MARE)has become a hot topic in recent years due to its broad applications.In this paper,based on the alternately linearized implicit iteration method(ALI)[Z.-Z.Bai et al.,Numer.Linear Algebra Appl.,13(2006),655-674.],we propose a new alternately linearized implicit iteration method(NALI)for computing the minimal nonnegative solution of M-matrix algebraic Riccati equation.Convergence of the NALI method is proved by choosing proper parameters for the MARE associated with nonsingular M-matrix or irreducible singular M-matrix.Theoretical analysis and numerical experiments show that the NALI method is more efficient than the ALI method in some cases.

关 键 词：M-matrix algebraic Riccati equation M-MATRIX ALI iteration method 

分 类 号：O15[理学—数学]