一类计算M-矩阵平方根的二次收敛算法

A CLASS OF QUADRATIC CONVERGENCE ALGORITHM FOR CALCULATING THE SQUARE ROOT OF M-MATRIX

矩阵的平方根广泛出现在科学计算和工程应用的很多领域中,本文研究了M-矩阵平方根的数值算法.基于一类简单的位移变换,将M-矩阵平方根的计算转化为M-矩阵代数Riccati方程的求解,并提出了一类迭代法以计算M-矩阵代数Riccati方程.理论分析显示,新方法具有二次收敛率.数值实验表明,新方法是可行的,而且在一定情况下也是较为有效的.

The square root of matrix is widely used in many fields of scientific calculation and engineering application.In this paper,the numerical algorithm for the square root of M-matrix is studied.Based on a kind of simple displacement transformation,the square root of M-matrix is transformed into the solution of M-matrix algebraic Riccati equation.A class of iterative method is proposed to calculate the M-matrix algebraic Riccati equation.Theoretical analysis shows that the new method has quadratic convergence rate.Numerical experiments show that the new method is feasible and effective in some cases.