中文摘要：

设P是大于1的偶数．本文基于方程xp-1=0的Newton和Halley求根公式给出计算非奇异矩阵酉极因子的数值方法，并证明算法的收敛性．用数值列子说明算法的有效性．

英文摘要：

Let p 〉 1 be an even number. In this paper, based on solving the equation xp - 1 = 0 we present the Newton iteration and Halley iteration to compute the polar decomposition of a nonsingular matrix, and prove their convergence properties. Numerical examples show that these algorithms are valid.