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线性流形上一类矩阵方程的最佳逼近问题

雷渊,廖安平   

  1. 湖南大学数学与计量经济学院;湖南大学数学与计量经济学院 长沙410082;长沙410082 长沙大学数学与信息科学系;长沙410003
  • 出版日期:2007-01-20 发布日期:2007-01-20

雷渊,廖安平. 线性流形上一类矩阵方程的最佳逼近问题[J]. 数值计算与计算机应用, 2007, 28(1): 1-10.

THE BEST APPROXIMATE PROBLEM OF A CLASS OF MATRIX EQUATION ON THE LINEAR MANIFOLD

  1. Lei Yuan (College of Mathematics and Econometrics,Hunan University,Changsha 410082,China) Liao Anping (College of Mathematics and Econometrics, Hunan University,Changsha 410082,China;Department of Mathematics and Information Sciences,Changsha University,Changsha 410003,China)
  • Online:2007-01-20 Published:2007-01-20
本文研究矩阵方程AXB=C在线性流形Γ={X∈SR~(n×n)|||TX-Y||=min}上的最佳逼近问题,得到了问题解的表达式.此外,还给出了求解该问题的数值算法和算例.
In this paper,the best approximate problem of the matrix equation AXB=C is studied on the manifoldΓ={X∈SR~(n×n)|||TX-Y||=min}.At the same time, the expression of the best approximate solution and the corresponding numerical method axe also given,and a numerical example is used to show the feasibility of this method.
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