华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 39-46.

• 应用数学与基础数学 • 上一篇    下一篇

四元数量子理论中最小二乘问题的代数方法

凌思涛$^{1, 2}$, 姜同松$^2$, 魏木生$^{1, 3}   

  1. 1. ~华东师范大学~~数学系, ~上海 200241; 2. ~临沂师范学院~~数学系, ~山东~临沂 276005;} \ZDWEI{ 3. ~上海师范大学~~数学系, ~上海 200234
  • 收稿日期:2008-09-06 修回日期:2008-12-06 出版日期:2009-07-25 发布日期:2009-07-25
  • 通讯作者: 魏木生

Algebraic method for least squares problems in quaternionic quantum theory

LING Si-tao$^{1, 2}$, JIANG Tong-song$^2$, WEI Mu-sheng$^{1, 3}

  

  1. 1. {\it Department of Mathematics, East China Normal University, Shanghai} 200241, {\it China};} \DWEI{2. {\it Department of Mathematics, Linyi Normal University, Linyi Shandong} 276005, {\it China};} \DWEI{3. {\it Department of Mathematics, Shanghai Normal University, Shanghai} 200234
  • Received:2008-09-06 Revised:2008-12-06 Online:2009-07-25 Published:2009-07-25
  • Contact: WEI Mu-sheng

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摘要： 借助四元数矩阵的复表示, 引进四元数矩阵范数, 研究四元数最小二乘
问题并得到了在四元数量子理论中解决四元数最小二乘问题的一种代数方法.
数值算例说明了算法的有效性.

关键词: 四元数最小二乘, 复表示, 法方程, 四元数最小二乘, 复表示, 法方程

Abstract: This paper introduced concepts of norms of quaternion matrices by means of
complex representation of a quaternion matrix, studied the quaternionic least squares
(QLS) problem and derived an algebraic method of finding solutions of the QLS problem in
quaternionic quantum theory. A numerical example verified the efficiency of the
algorithm.

Key words: complex representation, normal equation , quaternionic least squares, complex representation, normal equation

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