华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 47-53.

• 应用数学与基础数学 • 上一篇    下一篇

广义不定最小二乘问题的扰动分析

王茜

  

  1. 华东师范大学~~数学系,\; 上海 200062
  • 收稿日期:2008-11-06 修回日期:2009-02-06 出版日期:2009-07-25 发布日期:2009-07-25
  • 通讯作者: WANG Qian

Perturbation analysis for generalized indefinite least squares problems

WANG Qian   

  1. Department of Mathematics, East China Normal University,\; Shanghai}\quad 200062, {\it China}
  • Received:2008-11-06 Revised:2009-02-06 Online:2009-07-25 Published:2009-07-25
  • Contact: 王茜

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摘要： 通过定义一种新的加权广义逆，研究不定最小二乘问题和等式约束不定最小二乘问题。应用矩阵的双曲QR分解，
得到这两个问题的解的表达形式，并且推出了关于这两个问题的解的扰动界.

关键词: 扰动分析, 不定最小二乘问题, 等式约束不定最小二乘问题, 加权广义逆 , 扰动分析, 不定最小二乘问题, 等式约束不定最小二乘问题, 加权广义逆

Abstract: A new kind of weighted generalized inverse was defined to study indefinite
least squares (ILS) problem and equality constrained indefinite least squares (ILSE)
problem. By applying hyperbolic-QR factorization, the solutions to the two problems were
obtained. Also the perturbation bounds of the solutions were derived.

Key words: indefinite least squares problem, equality constrained indefinite least squares problem, weighted generalized inverse , perturbation analysis, indefinite least squares problem, equality constrained indefinite least squares problem, weighted generalized inverse

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