Perturbation Bounds for Subunitary Polar Factors of Extended Matrix under Non-preserving Perturbation

Wu Qiang

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Perturbation Bounds for Subunitary Polar Factors of Extended Matrix under Non-preserving Perturbation

更新时间：2026-05-27

- Perturbation Bounds for Subunitary Polar Factors of Extended Matrix under Non-preserving Perturbation
- Vol. 26, Issue 3, Pages: 86-89(2009)
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- Online First：02 October 2009，
  
  Published：2009
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吴强. 延拓矩阵在非保秩扰动下次酉极因子的扰动界[J]. 广东工业大学学报, 2009, 26(3): 86-89.

Wu Qiang. Perturbation Bounds for Subunitary Polar Factors of Extended Matrix under Non-preserving Perturbation[J]. 2009, 26(3): 86-89.
吴强. 延拓矩阵在非保秩扰动下次酉极因子的扰动界[J]. 广东工业大学学报, 2009, 26(3): 86-89. DOI：

Wu Qiang. Perturbation Bounds for Subunitary Polar Factors of Extended Matrix under Non-preserving Perturbation[J]. 2009, 26(3): 86-89. DOI：

摘要

延拓矩阵Rk(A)与其扰动矩阵R~k(A)的秩不相等时

利用奇异值分解的方法和在Frobenius范数下

对延拓矩阵Rk(A)与其扰动矩阵R~k(A)在广义极分解中的次酉因子

首次导出了在加法扰动下的扰动界和乘法扰动下的扰动界.

Abstract

When the extended matrix Rk(A) is not equal to its perturbation matrix R~k(A)

the perturbation bounds under additvie perburtation and multiplicatvie perturbation are deducted

by means of singualr value decomposition

the decomposited subunitary facotrs of the extended matrix Rk(A)

and its perturbation matrix R~k(A) in generalized polar decomposition under Frobenius norms.

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references

王震,蔺小林,蒋耀林. 行(或列)对称矩阵的满秩分解及其算法[J]. 高等学校计算数学学报. 2005(S1)

陈小山,黎稳. 酉不变范数下极分解的扰动界[J]. 计算数学. 2005(02)

邹红星,王殿军,戴琼海,李衍达. 延拓矩阵的奇异值分解[J]. 科学通报. 2000(14)

孙继广,陈春晖. 广义极分解[J]. 计算数学. 1989(03)

孙继广著.矩阵扰动分析[M]. 科学出版社, 1987

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