{"title":"An algebraic algorithm for the total least squares problem in commutative quaternionic theory","authors":"Tongsong Jiang , Dong Zhang , Zhenwei Guo , V.I. Vasil'ev","doi":"10.1016/j.amc.2024.129268","DOIUrl":null,"url":null,"abstract":"<div><div>A commutative quaternion total least squares (CQTLS) problem is a method of solving overdetermined sets of linear equations <span><math><mi>A</mi><mi>X</mi><mo>≈</mo><mi>B</mi></math></span> with errors in the matrices <em>A</em> and <em>B</em>. 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.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129268"},"PeriodicalIF":3.5000,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S009630032400729X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A commutative quaternion total least squares (CQTLS) problem is a method of solving overdetermined sets of linear equations 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.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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