An efficient iterative algorithm for finding a nontrivial symmetric solution of the Yang-Baxter-like matrix equation

Volume 12, Issue 1, pp 21--29 http://dx.doi.org/10.22436/jnsa.012.01.02

Publication Date: September 29, 2018 Submission Date: June 18, 2018 Revision Date: August 08, 2018 Accteptance Date: August 16, 2018

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Authors

Chacha Stephen Chacha - Mathematics department, Mkwawa University College of Education, (A constituent College of the University of Dar es salaam), P. O. Box 2513, Iringa, Tanzania. Hyun-Min Kim - Mathematics department, Pusan National University, Busan, 46241, Republic of Korea.

Abstract

This paper presents an efficient iterative method to obtain a nontrivial symmetric solution of the Yang-Baxter-like matrix equation \(AXA=XAX \). Necessary conditions for the convergence of the propounded iterative method are derived. Finally, three numerical examples to illustrate the efficiency of the proposed method and the preciseness of our theoretical results are provided.

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Keywords

• Yang-Baxter matrix equation
• iterative method
• nontrivial solution
• Newton's method

MSC

•  15A24
•  65F10
•  65H10

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