酉对称矩阵的极分解

doi:10.12341/jssms12127

系统科学与数学 ›› 2013, Vol. 33 ›› Issue (6): 740-750.DOI: 10.12341/jssms12127

• 论文 • 上一篇

酉对称矩阵的极分解

袁晖坪，郭伟，万波

重庆工商大学电子商务及供应链系统重庆市重点实验室, 重庆 400067; 重庆工商大学数学与统计学院, 重庆 400067

收稿日期:2012-02-16 出版日期:2013-06-25 发布日期:2013-08-30

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袁晖坪，郭伟，万波. 酉对称矩阵的极分解[J]. 系统科学与数学, 2013, 33(6): 740-750.

YUAN Huiping, GUO Wei, WAN Bo. THE POLAR FACTORIZATION FOR UNITARY SYMMETRIC MATRIX[J]. Journal of Systems Science and Mathematical Sciences, 2013, 33(6): 740-750.

THE POLAR FACTORIZATION FOR UNITARY SYMMETRIC MATRIX

YUAN Huiping, GUO Wei, WAN Bo

Chongqing Key Laboratory of Electronic Commerce and Supply Chain System, Chongqing Technology and Business University, Chongqing 400067; College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received:2012-02-16 Online:2013-06-25 Published:2013-08-30

为了简化大型行(列)酉对称矩阵的极分解, 研究了酉对称矩阵的性质, 获得了一些新的结果, 给出了酉对称矩阵的极分解和广义逆的公式, 它们可极大地减少行(列)酉对称矩阵的极分解的计算量与存储量, 并且不会丧失数值精度.同时对酉对称矩阵的极分解作了扰动分析.

To simplify the polar factorization of row (column) unitary symmetric matrix, the properties of row (column) unitary symmetric matrix were studied, and some new results were gained. The formula of the polar factorization and generalized inverse of row (column) unitary symmetric matrix were obtained, all of which can draatically reduce the aount of calculation and polar factorization of row (column) unitary symmetric matrix can dramatically save the CPU time and memory without losing any numerical precision. Some perturbation bounds of the polar factor were presented.

Key words: font-size: 9pt" lang="EN-US">Unitary symmetric matrix, polar factorization, generalized inverse, perturbation bound.

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