申 盼，張乃敏

(溫州大學數學與信息科學學院，浙江溫州 325035)

關于加權廣義逆在F范數下的最優(yōu)擾動界

申 盼，張乃敏

(溫州大學數學與信息科學學院，浙江溫州 325035)

利用加權奇異值分解技術和加權廣義逆的性質，推廣了有關文獻關于廣義逆A+在F范數下的最優(yōu)擾動界的相關結論，分兩種情況，給出了加權廣義逆在F范數下的最優(yōu)擾動界.

加權廣義逆；加權奇異值分解；F范數；擾動界

1 相關引理

2 最優(yōu)擾動界

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[3]Wedin P-A. Perturbation bounds in connection with singular value decomposition [J]. BIT, 1972, 12: 99-111.

[4]Wei Y M, Wu H B. Expression for the perturbation of the Weighted Moore-Penrose inverse [J]. J Comput Appl Math, 2000, 39: 13-18.

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[8]陳小山, 黎穩(wěn). 次酉極因子在酉不變范數下的相對擾動界[J]. 數學進展, 2000, 39: 13-18.

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

(編輯：王一芳)

O241.6

A

1674-3563(2011)04-0005-07加權廣義逆對求解不相容線性方程組的極小N范數M最小二乘解有非常重要的意義.文獻[1-3]給出了廣義逆A+以及加權廣義逆在一些酉不變范數下的擾動界.文獻[4]給出了加權廣義逆擾動的一種表達式.最近，鄭兵等又通過奇異值分解，給出了廣義逆A+在F范數下的最優(yōu)擾動界[5].本文將通過加權奇異值分解，來討論加權廣義逆在F范數下的最優(yōu)擾動界，以此來進一步完善加權廣義逆在酉不變范數下的某些擾動性質.

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

2010-10-13

申盼(1986- )，男，河南焦作人，碩士研究生，研究方向：計算機數學