An E-extra iteration method for solving reduced biquaternion matrix equation $ AX+XB = C

This paper focuses on the solution of the reduced biquaternion equation $ AX+XB = C $ using the E-extra iteration method. By utilizing the complex decomposition of a reduced biquaternion matrix, we transform the equation into a complex matrix equation. Subsequently, we analyze the convergence of thi...

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Published inAIMS mathematics Vol. 9; no. 7; pp. 17578 - 17589
Main Authors Lan, Jiaxin, Huang, Jingpin, Wang, Yun
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
complex decomposition
convergence analysis
e-extra iteration method
numerical example
reduced biquaternion
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ISSN2473-6988
2473-6988
DOI10.3934/math.2024854

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Abstract This paper focuses on the solution of the reduced biquaternion equation $ AX+XB = C $ using the E-extra iteration method. By utilizing the complex decomposition of a reduced biquaternion matrix, we transform the equation into a complex matrix equation. Subsequently, we analyze the convergence of this method and provide guidelines for selecting optimal parameters. Finally, numerical examples are presented to demonstrate the efficacy of our algorithm.
AbstractList This paper focuses on the solution of the reduced biquaternion equation $ AX+XB = C $ using the E-extra iteration method. By utilizing the complex decomposition of a reduced biquaternion matrix, we transform the equation into a complex matrix equation. Subsequently, we analyze the convergence of this method and provide guidelines for selecting optimal parameters. Finally, numerical examples are presented to demonstrate the efficacy of our algorithm.
Author Huang, Jingpin
Wang, Yun
Lan, Jiaxin
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SubjectTerms complex decomposition
convergence analysis
e-extra iteration method
numerical example
reduced biquaternion
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Title An E-extra iteration method for solving reduced biquaternion matrix equation $ AX+XB = C
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