符号函数法的算法改进──快速符号函数法

The Improvement of Matrix Sign Function Method一the Fast Matrix Function Method

在进行线性二次型控制系统最优控制设计时，需要求解黎卡提方程。近年来人们对符号函数法求解黎卡提代数方程给予了更多的重视，这种算法的特点是收敛速度快，不需选择初值阵Ｐ０，且编程容易。本文就加速因子给出了新的选取方法，使得迭代式收敛速度十分令人满意。

In this paper,the author proposes a new method to determine the accelerating factor in the matrix sign func-tion method.The convergence speed of the new method is satisfactory.How to solve both continuous algebraicRiccati equation and discrete algebraic Riccati equation by use of the sign function is also discussed in this paper。