L-structure least squares solutions of reduced biquaternion matrix equations with applications

2023/11/11 by Sk. Safique Ahmad, Ahmad, Sk. Safique, Neha Bhadala +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2311.06461

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

Abstract

This paper presents a framework for computing the structure-constrained least squares solutions to the generalized reduced biquaternion matrix equations (RBMEs). The investigation focuses on three different matrix equations: a linear matrix equation with multiple unknown L-structures, a linear matrix equation with one unknown L-structure, and the general coupled linear matrix equations with one unknown L-structure. Our approach leverages the complex representation of reduced biquaternion matrices. To showcase the versatility of the developed framework, we utilize it to find structure-constrained solutions for complex and real matrix equations, broadening its applicability to various inverse problems. Specifically, we explore its utility in addressing partially described inverse eigenvalue problems (PDIEPs) and generalized PDIEPs. Our study concludes with numerical examples.

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