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Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory
Author(s) -
Wang Gang,
Guo Zhenwei,
Zhang Dong,
Jiang Tongsong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5917
Subject(s) - quaternion , mathematics , quaternionic representation , algebraic number , algebra over a field , unification , representation (politics) , real algebraic geometry , least squares function approximation , quaternion algebra , real representation , algebra representation , pure mathematics , mathematical analysis , division algebra , geometry , computer science , irreducible representation , statistics , estimator , politics , political science , law , programming language
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.