Iterative algorithm for the reflexive solutions of the generalized Sylvester matrix equation

• Main Authors: Mohamed A. Ramadan, Naglaa M. El–shazly, Basem I. Selim
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: Journal of the Egyptian Mathematical Society
• Subjects: Generalized Sylvester matrix equation; Iterative method; Reflexive matrices; Least Frobenius norm solution
• Online Access: http://link.springer.com/article/10.1186/s42787-019-0030-0

Abstract In this paper, the generalized Sylvester matrix equation AV + BW = EVF + C over reflexive matrices is considered. An iterative algorithm for obtaining reflexive solutions of this matrix equation is introduced. When this matrix equation is consistent over reflexive solutions then for any initial reflexive matrix, the solution can be obtained within finite iteration steps. Furthermore, the complexity and the convergence analysis for the proposed algorithm are given. The least Frobenius norm reflexive solutions can also be obtained when special initial reflexive matrices are chosen. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithm.