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广义逆A_(T,S)^((2))的扰动界 被引量：2

The Optimal Perturbation Bounds for the Generalized Inverse A_(T,S)^((2))
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摘要 利用奇异值分解和A_(T,S)^((2))与Moore-Penrose广义逆的关系,给出广义逆A_(T,S)^((2))在酉不变范数下的扰动界,推广了Moore-Penrose广义逆在酉不变范数下的某些结果. We obtain the perturbation bounds of the generalized inverse AT,S（2） with respect to the unitarily invariantnorm by using Singular Value Decomposition and the relation of AT,S（2） and Moore-Penrose, which extend some recent results of Moore-Penrose under unitarily invariant norm.
作者 杨晓英 朱清溢 刘新
机构地区 四川信息职业技术学院基础教育部 电子科技大学物理电子学院
出处 《北华大学学报（自然科学版）》 CAS 2013年第2期146-149,共4页 Journal of Beihua University（Natural Science）
基金 中央高校基本科研业务费专项资金项目(ZYGX2011YB020)
关键词 酉不变范数 谱范数 广义逆 扰动界 unitarily invariant norm spectral norm generalized inverse perturbation bound
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Cai L X, Xu W W, LI W. Additive and Multiplicative Perturbation Bounds for the Moore-Penrose Inverse [ J ]. Linear Algebra and Its Applications ,2011,434:480-489.
  • 2Meng L S,Zheng B. The Optimal Perturbation Bounds of the Moore-Penrose Inverse Under the Frobenius Norm [ J ]. Linear Algebra and Its Applications,2010,432:956-963.
  • 3Xu W W, Cai L X,Li W. The Optimal Perturbation Bounds for the Weighted Moore-Penrose Inverse [ J ]. Electronic Journal of Linear Algebra,2011,22:521-538.
  • 4Liu X J, Qin Y H, Yu Y M. Perturbation Bounds for the Generalized Inverse A^(2)T,S with Respect to the Frobenius Norm [ J ].Applied Mathematics and Computation ,2011,218:4595-4604.
  • 5Zhang N M,Wei Y M. Perturbation Bounds for the Generalized Inverses A^(2)T,S with Application to Constrained Linear System [ J ].Applied Mathematics and Computation ,2003,142:63-78.
  • 6Yimin Wei, Hebing Wu. On the Perturbation and Subpmper Splittings for the Generalized Inverse A^(2)T,S of Rectangular Matrix A [ J ]. Journal of Computational and Applied Mathematics,2001,137:317-329.
  • 7Liu G, Lu S Q, Chen J P,et al. A Note on Condition Numbers for Generalized Inverse A^(2)T,S and Constrained Linear Systems [ J ].Applied Mathematics and Computation,2010,217:3199-3206.

同被引文献7

  • 1Wang S F,Zheng B,Xiong Z P. The Condition Numbers for Weighted Moore-Penrose Inverse and Weighted Linear Least Squares Problem[J].Applied Mathematics and Computation,2009.197-205.
  • 2Liu G,Lu S Q,Chen J P. A Note on Condition Numbers for Generalized Inverse and Constrained Linear Systems[J].Applied Mathematics and Computation,2010.3199-3206.
  • 3Zhang N M,Wei Y M. Perturbation Bounds for the Generalized Inverses with Application to Constrained Linear Systems[J].Applied Mathematics and Computation,2003.63-78.
  • 4Wei Y M,Wu H B. On the Perturbation and Subproper Splittings for the Generalized Inverse of Rectangular Matrix A[J].Journal of Computational and Applied Mathematics,2001.317-329.
  • 5程云鹏;张凯院;徐仲.矩阵论[M]西安:西北工业大学出版社,2006290-295.
  • 6Liu X J,Qin Y H,Yu Y M. Perturbation Bounds for the Generalized Inverse with Respect to the Frobenius Norm[J].Applied Mathematics and Computation,2011.4595-4604.
  • 7魏益民,王国荣.广义逆A_T^((2)),S的扰动理论(英文)[J].复旦学报（自然科学版）,2000,39(5):482-488. 被引量：3

引证文献2

北华大学学报（自然科学版）
2013年 第2期

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