關(guān)于加權(quán)廣義逆在F范數(shù)下的最優(yōu)擾動界

申 盼，張乃敏

(溫州大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院，浙江溫州 325035)

關(guān)于加權(quán)廣義逆在F范數(shù)下的最優(yōu)擾動界

申 盼，張乃敏

(溫州大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院，浙江溫州 325035)

利用加權(quán)奇異值分解技術(shù)和加權(quán)廣義逆的性質(zhì)，推廣了有關(guān)文獻關(guān)于廣義逆A+在F范數(shù)下的最優(yōu)擾動界的相關(guān)結(jié)論，分兩種情況，給出了加權(quán)廣義逆在F范數(shù)下的最優(yōu)擾動界.

加權(quán)廣義逆；加權(quán)奇異值分解；F范數(shù)；擾動界

1 相關(guān)引理

2 最優(yōu)擾動界

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[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.

[5]Meng L S, Zheng B. The optimal perturbation bounds of Moore-Penrose inverse under the Frobenius norm [J]. Linear Algebra Appl, 2010, 432: 956-963.

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[8]陳小山, 黎穩(wěn). 次酉極因子在酉不變范數(shù)下的相對擾動界[J]. 數(shù)學(xué)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(quán)廣義逆對求解不相容線性方程組的極小N范數(shù)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(quán)廣義逆在一些酉不變范數(shù)下的擾動界.文獻[4]給出了加權(quán)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(shù)下的最優(yōu)擾動界[5].本文將通過加權(quán)奇異值分解，來討論加權(quán)廣義逆在F范數(shù)下的最優(yōu)擾動界，以此來進一步完善加權(quán)廣義逆在酉不變范數(shù)下的某些擾動性質(zhì).

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(shù)學(xué)