Perturbation Bounds for Singular Space of Extended Matrix-under Multiplicative Perturbation

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Perturbation Bounds for Singular Space of Extended Matrix-under Multiplicative Perturbation

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- Perturbation Bounds for Singular Space of Extended Matrix-under Multiplicative Perturbation
- Vol. 28, Issue 1, Pages: 58-61(2011)
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- Published：2011
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文伟. 在乘法扰动下延拓矩阵奇异空间的扰动界[J]. 广东工业大学学报, 2011, 28(1): 58-61.

WEN Wei. Perturbation Bounds for Singular Space of Extended Matrix-under Multiplicative Perturbation[J]. 2011, 28(1): 58-61.
文伟. 在乘法扰动下延拓矩阵奇异空间的扰动界[J]. 广东工业大学学报, 2011, 28(1): 58-61. DOI：

WEN Wei. Perturbation Bounds for Singular Space of Extended Matrix-under Multiplicative Perturbation[J]. 2011, 28(1): 58-61. DOI：

摘要

在矩阵A和A~有相同分块的奇异值分解和乘法扰动下，对于母矩阵为A的行延拓矩阵Rk(A)与其扰动矩阵R~k(A~)，使用奇异值的双分离度获得左右奇异空间的分离，研究了延拓矩阵Rk(A)与其扰动矩阵R~k(A~)的奇异空间在Frobenius范数下的扰动界.

Abstract

When Matrix A and A~Matrix have the same partition singular decomposition and multiplicative perturbations

the Extended Matrix Rk(A) with mother Matrix A and the Extended Matrix R~k(A~) with mother Matrix A~

the seperation between the left singular space and the right singular space is obtained by using double seperation degree.Furthermore

the perturbation bounds for the singular space of the Extended Matrix Rk(A) and its perturbation matrix R~k(A~) are studied under Frobenius norm.

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references

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邹红星，王殿军，戴琼海,等.延拓矩阵的奇异值分解[J].科学通报，2000,45(14)：1560-1562.

陈小山.矩阵特征空间和奇异空间相对扰动界[J].华南师范大学学报,2005(1): 6-10.

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Davis C,Kahan W.The rotation of eigenvectors by a perturbation(Ⅲ),SIAM[J].Numer.Anal,1970(7):1-46.

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