非对称代数Riccati方程的一类不精确迭代解法

A class of inexact iterative method for nonsymmetric algebraic Riccati equations

研究了非对称代数Riccati方程的数值解法.不动点迭代法是求解非对称代数Riccati方程的一类经典算法,然而不动点迭代法在每步迭代中都需要求解一个Sylvester方程,因此运算量比较大.本文对一类不动点迭代法进行了改进,提出了不精确迭代法以求解方程,该方法在外层迭代中使用不动点迭代法,而在内层迭代求解Sylvester方程时使用了Smith算法,进而减少了运算量.理论分析和数值实验表明,本文所提的方法是可行的,而且与基本的不动点迭代法相比,也是较为有效的.

In this paper,numerical solution of the nonsymmetric algebraic Riccati equation is studied.The fixed point iterative method is a classical algorithm for solving nonsymmetric algebraic Riccati equations.However,the fixed point iterative method needs to solve a Sylvester equation in each iteration,so the computation is relatively large.In this paper,a kind of fixed point iteration method is improved,and an inexact iteration method is proposed to solve the equation.In this method the fixed point iteration method is used in the outer iteration,while Smith algorithm is used in the inner iteration to solve the Sylvester equation,thus reducing the computational complexity.Theoretical analysis and numerical experiments show that the proposed method is feasible and is more effective than the basic fixed point iteration method.