Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory. (2nd December 2019)

• Record Type: Journal Article
• Authors: Wang, Gang; Guo, Zhenwei; Zhang, Dong; Jiang, Tongsong
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 3(2020)
• Page Start: 1124
• Page End: 1137
• Publication Date: 2019-12-02
• Subjects: complex representation -- generalized quaternion -- least squares problem -- quaternion -- real representation -- split quaternion; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5917
• Languages: English
• ISSNs: 0170-4214

Abstract

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.