关于加权广义逆在F范数下的最优扰动界

申 盼，张乃敏

(温州大学数学与信息科学学院，浙江温州 325035)

关于加权广义逆在F范数下的最优扰动界

申 盼，张乃敏

(温州大学数学与信息科学学院，浙江温州 325035)

利用加权奇异值分解技术和加权广义逆的性质，推广了有关文献关于广义逆A+在F范数下的最优扰动界的相关结论，分两种情况，给出了加权广义逆在F范数下的最优扰动界.

加权广义逆；加权奇异值分解；F范数；扰动界

1 相关引理

2 最优扰动界

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Study on Optimal Perturbation Bounds of Weighted Generalized Inverseunder Frobenius Norm

SHEN Pan, ZHANG Naimin
(College of Mathematics and Information Science, Wenzhou University, Wenzhou, China 325035)

Based on the weighted singular value decomposition and properties of weighted generalized inverse, conclusions in many documents about optimal perturbation bounds of generalized inverseA+were further introduced. Furthermore, from two aspects, the optimal perturbation bound of weighted generalized inverseunder the Frobenius norm was analyzed and obtained.

Weighted Generalized Inverse; Weighted Singular Value Decomposition; Frobenius Norm; Perturbation Bound

(编辑：王一芳)

O241.6

A

1674-3563(2011)04-0005-07加权广义逆对求解不相容线性方程组的极小N范数M最小二乘解有非常重要的意义.文献[1-3]给出了广义逆A+以及加权广义逆在一些酉不变范数下的扰动界.文献[4]给出了加权广义逆扰动的一种表达式.最近，郑兵等又通过奇异值分解，给出了广义逆A+在F范数下的最优扰动界[5].本文将通过加权奇异值分解，来讨论加权广义逆在F范数下的最优扰动界，以此来进一步完善加权广义逆在酉不变范数下的某些扰动性质.

10.3875/j.issn.1674-3563.2011.04.002 本文的PDF文件可以从xuebao.wzu.edu.cn获得

2010-10-13

申盼(1986- )，男，河南焦作人，硕士研究生，研究方向：计算机数学