离散耦合Riccati矩阵方程解的上下界估计及其不动点迭代算法  

The Upper and Lower Matrix Bounds and Fixed Point Iteration Algorithm of the Discrete Coupled Algebraic Riccati Equation

作　　者：张娟[1] 李世凤 张争争 ZHANG Juan;LI Shi-feng;ZHANG Zheng-zheng(Department of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105 China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《湘潭大学学报（自然科学版）》2019年第1期37-48,共12页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金项目(11771370;11571292);湖南省自然科学基金项目(2018JJ2376;2017JJ3305);湖南省教育厅项目(16B257)

摘　　要：利用M-矩阵及其逆的特殊性质,讨论了离散耦合代数Riccati矩阵方程正定解的上下界.进一步,获得了这类方程解的存在唯一性条件和不动点迭代算法.最后,给出相应的数值例子来说明所得结果的有效性.In this paper,using the special properties of M-matrix and its inverse matrix,we discuss the upper and lower matrix bounds for the solution of the discrete coupled algebraic Riccati equation.Further,we present the existence uniqueness and the fixed point iteration algorithm of this equation.Finally,we offer corresponding numerical examples to illustrate the effectiveness of the derived results.

关 键 词：离散耦合代数Riccati矩阵方程 矩阵界 不动点迭代算法 

分 类 号：O241.6[理学—计算数学]