矩阵极分解计算的一个注记

设$p$是大于$1$的偶数,根据方程$x^{-p}-1=0$的Newton求根公式, 给出计算非奇异矩阵酉极因子的数值方法,并证明了它具有二次收敛特性. 数值例子表明该算法是有效的.

A Note on Computing the Polar Decomposition

Let $p$ be an even number greater than $1$. In this paper, based on the Newton method for solving the equation $x^{-p}-1=0$, the new numerical method is proposed to compute the polar decomposition of a nonsingular matrix and its quadratic convergence is proved. Numerical examples show that this numerical method is efficient.