迭代法求解复非对称代数Riccati方程

Iterative Methods for Complex Nonsymmetric Algebraic Riccati Equations

近年来,复非对称代数Riccati方程越来越受到专家和学者的关注,本文主要考虑复非对称代数Riccati方程的求解问题。本文首先讨论了复非对称代数Riccati方程极值解的存在唯一性,证得了在Q的比较矩阵Q是非奇异M矩阵的假设条件下,复非对称代数Riccati方程存在唯一的极值解,并且该解可由牛顿法和不动点迭代法求得,最后通过数值实验表明这两种算法是有效可行的。

In recent years,the complex nonsymmetric algebraic Riccati equation has attracted more and more attention of experts and scholars.In this paper,we consider the complex nonsymmetric algebraic Riccati equation,which arises in Markov modulated fluid flow.Firstly,an extended condition of the existence and uniqueness of the extremal solution to these equations are proved,in other words,we proved that the complex nonsymmetric algebraic Riccati equation has the extremal solution when the comparison matrix Q is a nonsingular M-matrix.Then the fixed-point method and Newton's method are presented to find the extremal solution.Two numerical examples are given to illustrate the effectiveness of two methods.