Algebraic technique for mixed least squares and total least squares problem in the reduced biquaternion algebra

2023/11/11 by Sk. Safique Ahmad, Ahmad, Sk. Safique, Neha Bhadala +1
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2311.06464

openalex publication_date 2023/11/11 · openalex created_date 2023/11/15 · openalex updated_date 2026/07/28

Abstract

This paper presents the reduced biquaternion mixed least squares and total least squares (RBMTLS) method for solving an overdetermined system AX ≈ B in the reduced biquaternion algebra. The RBMTLS method is suitable when matrix B and a few columns of matrix A contain errors. By examining real representations of reduced biquaternion matrices, we investigate the conditions for the existence and uniqueness of the real RBMTLS solution and derive an explicit expression for the real RBMTLS solution. The proposed technique covers two special cases: the reduced biquaternion total least squares (RBTLS) method and the reduced biquaternion least squares (RBLS) method. Furthermore, the developed method is also used to find the best approximate solution to AX ≈ B over a complex field. Lastly, a numerical example is presented to support our findings.

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