Least-Squares Solutions of Generalized Sylvester-Type Quaternion Matrix Equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-05-08 DOI:10.1007/s00006-023-01276-w

Sinem Şimşek

引用次数: 0

Abstract

This paper focuses on finding solutions of generalized Sylvester-type matrix equations over the quaternion skew-field. We express the general least–squares solutions, and perhermitian, skew-perhermitian least-squares solutions of \(AXB+CYD=E\) and \(AXB+CXD=E\) over the quaternion skew-field in terms of a vec operator (defined specifically for matrices over the quaternion skew-field) and the Moore–Penrose pseudoinverse. In addition, characterizations that facilitate the computation of the least-squares solutions closest to prescribed quaternion matrices are deduced. We illustrate our theoretical findings on several numerical examples, most of which originate from color image restoration via Tikhonov regularization.

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广义sylvester型四元数矩阵方程的最小二乘解

本文主要研究四元数斜场上广义Sylvester型矩阵方程的解。我们用向量算子（专门为四元数斜场上的矩阵定义）和Moore–Penrose伪逆表示四元数偏斜场上\（AXB+CYD=E\）和\（AXB+CXD=E\）的一般最小二乘解和全ermitian、斜全ermitia最小二乘解。此外，还推导了便于计算最接近规定四元数矩阵的最小二乘解的特征。我们在几个数值例子中说明了我们的理论发现，其中大多数来自于通过Tikhonov正则化的彩色图像恢复。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.