含高次逆幂的矩阵方程对称解的双迭代算法

DOUBLE ITERATIVE ALGORITHM FOR SYMMETRIC SOLUTION OF MATRIX EQUATION WITH HIGH ORDER INVERSE-POWER

本文研究了在控制理论和随机滤波等领域中遇到的一类含高次逆幂的矩阵方程的等价矩阵方程对称解的数值计算问题.采用牛顿算法求等价矩阵方程的对称解,并采用修正共轭梯度法求由牛顿算法每一步迭代计算导出的线性矩阵方程的对称解或者对称最小二乘解,建立了求这类矩阵方程对称解的双迭代算法,数值算例验证了双迭代算法是有效的.

A new iterative algorithm is proposed to get the symmetric solution of equivalent matrix equation transformed from the matrix equation with high order inverse-power which is common in many fields such as control theory and stochastic filtering. By using Newton＇s method, we obtain symmetric solution of the above equivalent matrix equation, and with modified conjugate gradient method, we get symmetric solution or symmetric least square solution of linear matrix equation derived from each iterative step of Newton＇s method. A double iterative algorithm is proposed to solve the symmetric solution of this kind of matrix equation, and numerical experiments demonstrate the effectiveness of proposed double iterative method.