Newton法在计算矩阵p次根问题上的收敛性

On the convergence of Newton's method for computing the matrix p-th root

主要研究了Newton法在计算矩阵主p次根问题上的收敛性.通过复分析相关理论,得到了一个新的收敛域,并证明了当给定矩阵的所有特征值都落入该收敛域时,由Newton法迭代产生的矩阵序列平方收敛于该矩阵的主p次根.

It was considered the convergence region of Newton＇s method for computing the principal p-th root of a matrix. It was obtained a new convergence region by using the theory of complex analysis. It was showed that the Newton method converged to the principal p-th root quadratically when all the eigenvalues of the matrix located in this new region.