中文摘要：

M-矩阵代数Riccati方程由于广泛的应用,已成为近年来的热点问题之一,有关其理论和数值方法的研究层出不穷.本文研究M-矩阵代数Riccati方程的数值解法,给出求解其最小非负解的两种新的不动点迭代法.理论分析表明新的不动点迭代法相比现有的不动点迭代法收敛速度快,数值实验也验证了新方法的有效性.

英文摘要：

Research on the theories and the 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 we consider numerical solution of the MARE. We propose two new fixed-point iterative methods for computing the minimal nonnegative solution of MARE, which have smaller convergent rate than some previous fixed-point iterative methods. Theoretical analysis and numerical experiments are given to show that the new fixed-point iterative methods are effective and efficient.