Riccati方程子矩阵约束对称解的非精确Newton-MCG算法  

INEXACT NEWTON-MCG ALGORITHM FOR SYMMETRIC SOLUTION WITH A SUBMATRIX CONSTRAINT OF RICCATI MATRIX EQUATION

作　　者：梁志艳[1] 张凯院[1] 耿小姣 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《数值计算与计算机应用》2015年第4期288-296,共9页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11471262)

摘　　要：采用修正共轭梯度法(MCG算法)求由Newton算法每一步迭代计算导出的线性矩阵方程的近似子矩阵约束(SMC)对称解或者近似SMC对称最小二乘解,建立求离散时间代数Riccati矩阵方程SMC对称解的非精确Newton-MCG算法.该算法仅要求Riccati矩阵方程有SMC对称解,不要求它的SMC对称解唯一,也不要求导出的线性矩阵方程有相应的SMC对称解.数值算例表明,非精确Newton-MCG算法是有效的.In this paper, the inexact Newton-MCG algorithm for solving the symmetric solution with a submatrix constraint of the discrete-time algebraic Riccati equation is proposed. The algorithm is based on the MCG algorithm, which is applied to getting the approximate symmetric solution or the approximate symmetric least-square solution with a submatrix constraint of linear matrix equation derived from each Newton step. It only requires the Riccati equation to have the symmetric solution with a submatrix constraint, and the solution may not be unique. Moreover, it doesn＇t require the derived linear matrix equation to have the relevant solution. Numerical results illustrate the efficiency of the algorithm.

关 键 词：Riccati矩阵方程 子矩阵约束对称解 非精确Newton算法 MCG算法 非精确Newton—MCG算法 

分 类 号：O241.6[理学—计算数学]