Algebraic techniques for least squares problems in commutative quaternionic theory期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Algebraic techniques for least squares problems in commutative quaternionic theory

Authors:	Dong Zhang Zhenwei Guo Gang Wang Tongsong Jiang

Institution:	1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China;2. School of Mathematics and Statistics, Heze University, Heze China School of Mathematical Science, Liaocheng University, Liaocheng China;3. School of Mathematics and Statistics, Linyi University, Linyi China

Abstract:	Due to the rise of commutative quaternion in Hopfield neural networks, digital signal, and image processing, one encounters the approximate solution problems of the commutative quaternion linear equations $A ? X \approx B$ and $A ? X ? C \approx B$ . This paper, by means of real representation and complex representation of commutative quaternion matrices, introduces concepts of norms of commutative quaternion matrices and derives two algebraic techniques for finding solutions of least squares problems in commutative quaternionic theory.

Keywords:	commutative quaternion complex representation least squares problem matrix norm real representation