An accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations

Subject Areas : Linear and multilinear algebra; matrix theory

A‎. ‎M‎. ‎E‎. ‎ Bayoumi ¹ , M. A. Ramadan ² , M. Nili Ahmadabadi ³

1 - Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
2 - Department of Mathematics, Faculty of Science, Menoufia University, Shebeen El- Koom, Egypt
3 - Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Received: 2018-07-06 Accepted : 2019-01-29 Published : 2019-06-01

Keywords: Coupled matrix equations, Frobenius norm, relaxation parameters, gradient algorithm,

Abstract :

‎In this paper‎, ‎an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed‎. ‎The convergence analysis of the algorithm is investigated‎. ‎We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions‎. ‎Finally‎, ‎some numerical examples are given to demonstrate the behavior of the proposed method and to support the theoretical results of this paper‎.

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