Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory |
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| Authors: | Gang Wang Zhenwei Guo Dong Zhang Tongsong Jiang |
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| Institution: | 1. School of Mathematics and Statistics, Heze University, Heze, 274015 Shandong, PR China;2. School of Mathematical Science, Liaocheng University, Liaocheng, 252000 Shandong, PR China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590 Shandong, PR China |
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| Abstract: | This paper aims to present, in a unified manner, algebraic techniques for least squares problem in quaternionic and split quaternionic mechanics. This paper, by means of a complex representation and a real representation of a generalized quaternion matrix, studies generalized quaternion least squares (GQLS) problem, and derives two algebraic methods for solving the GQLS problem. This paper gives not only algebraic techniques for least squares problem over generalized quaternion algebras, but also a unification of algebraic techniques for least squares problem in quaternionic and split quaternionic theory. |
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| Keywords: | complex representation generalized quaternion least squares problem quaternion real representation split quaternion |
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