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矩阵极分解新的数值方法

温朝涛, 陈小山   

  1. 华南师范大学数学科学学院, 广州 510631
  • 收稿日期:2015-12-08 出版日期:2017-02-15 发布日期:2017-02-17
  • 基金资助:

    广东省自然科学基金(S2013010012530)资助和华南师范大学研究生科研创新基金(2015lkxm21)和国家自然科学基金(11671158)资助.

温朝涛, 陈小山. 矩阵极分解新的数值方法[J]. 计算数学, 2017, 39(1): 23-32.

Wen Chaotao, Chen Xiaoshan. NEW NUMERICAL METHODS FOR COMPUTING THE POLAR DECOMPOSITION[J]. Mathematica Numerica Sinica, 2017, 39(1): 23-32.

NEW NUMERICAL METHODS FOR COMPUTING THE POLAR DECOMPOSITION

Wen Chaotao, Chen Xiaoshan   

  1. School of Mathematics, South China Normal University, Guangzhou 510631, China
  • Received:2015-12-08 Online:2017-02-15 Published:2017-02-17
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.
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.

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