An algebraic algorithm for the total least squares problem in commutative quaternionic theory

A commutative quaternion total least squares (CQTLS) problem is a method of solving overdetermined sets of linear equations AX≈B with errors in the matrices A and B. In the theoretical studies and numerical calculations of commutative quaternionic theory, the CQTLS problem is an extremely effective...

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Vydáno v:Applied mathematics and computation Ročník 494; s. 129268
Hlavní autoři: Jiang, Tongsong, Zhang, Dong, Guo, Zhenwei, Vasil'ev, V.I.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.06.2025
Témata:
Commutative quaternion matrix
Real presentation
Singular value decomposition
Total least squares problem
Real presentation
Total least squares problem
Commutative quaternion matrix
Singular value decomposition
ISSN:0096-3003
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Shrnutí:A commutative quaternion total least squares (CQTLS) problem is a method of solving overdetermined sets of linear equations AX≈B with errors in the matrices A and B. In the theoretical studies and numerical calculations of commutative quaternionic theory, the CQTLS problem is an extremely effective tool for the study of telecommunications, geodesy, and image processing theory. This paper, by means of the real representation of a commutative quaternion matrix, studies the CQTLS problem, derives necessary and sufficient conditions for the CQTLS problem has a commutative quaternion solution, and gives an algebraic algorithm for solving the CQTLS problem. •A necessary and sufficient condition is given for solving the commutative quaternion total least squares (CQTLS) problem.•An algebraic algorithm is given for solving the total least squares problem of the commutative quaternion matrix.•The algebraic relations between the problem of the CQTLS and the problem of the real TLS are established.•Two numerical experiments demonstrate the correctness and efficiency of the algorithm for solving the CQTLS.
ISSN:0096-3003
DOI:10.1016/j.amc.2024.129268