Work

The Split Quaternion Least Squares Problem With Equality Constraint and Its Application

Year: 2025

Type: article

Abstract: ABSTRACT By applying the real representation matrix and the Moore–Penrose inverse of the split quaternion matrix, we first study the split quaternion least squares problem with equality constraint (SQLSE) and obtain its general solution and minimum norm solution. Then, we obtain the Karush–Kuhn–Tucker equation, which is an equivalent problem of the SQLSE problem. Immediately after, we propose a numerical algorithm on the real number field for the minimum norm solution of the SQLSE problem and enumerate three examples to display its validity. Eventually, we provide an application of the SQLSE problem in the color image restoration.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10967

Authors: Zhi‐Han Zhou, Zi‐Xiang Meng, Ying Li, Feng‐Xia Zhang

Institution: Liaocheng University

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Strong, Liaocheng University, Natural Science Foundation of Shandong Province

Awards: G4861881532, G5655394322