Algebraic algorithms for least squares problem in quaternionic quantum theory

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• 作者：Tongsong Jiang ; Li Chen
• 关键词：Least squares ; Quaternion matrix ; Algorithm ; Quaternionic quantum theory
• 刊名：Computer Physics Communications
• 出版年：2007
• 期刊代码：30_00104655
• 类别：cp
• 出版时间：1 April 2007
• 卷：176
• 期：7
• 页码：481-485
• 文件大小：146 K

摘要

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AX≈B that is appropriate when there is error in the matrix B. In this paper, by means of complex representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, discuss singular values and generalized inverses of a quaternion matrix, study the QLS problem and derive two algebraic methods for finding solutions of the QLS problem in quaternionic quantum theory.