In this paper, a relaxed gradient based algorithm for solving extended Sylvester-conjugate matrix equations by considering a relaxation parameter is proposed. The convergence analysis of the algorithm is investigated. Theoretical analysis shows that the new method converges under certain assumptions. A numerical example is given to illustrate effectiveness of the proposed method and to test its efficiency compared with an existing one.
In this paper, five iterative methods for solving two coupled fuzzy Sylvester matrix equations are considered. The two coupled fuzzy Sylvester matrix equations are expressed by using the generalized inverse of the coefficient matrix, then iterative solutions are constructed by applying the hierarchical identification principle and by using the block-matrix inner product (the star product for short). A proposed modification to this algorithm to solve the first coupled fuzzy Sylvester matrix equations is suggested. This proposed modification is compared with the first algorithm where our modification exhibits fast convergence behavior. Also, we suggested two leastsquares iterative algorithm by applying a hierarchical identification principle to solve the two coupled fuzzy Sylvester matrix equations. The proposed methods are illustrated by numerical examples.
In this paper, we consider explicit and iterative methods for solving the Generalized Sylvester matrix equation AV + BW = EVF + C. Based on the use of Kronecker map and Sylvester sum some lemmas and theorems are stated and proved where explicit and iterative solutions are obtained. The proposed methods are illustrated by numerical example. The obtained results show that the methods are very neat and efficient.
In this paper, we present an accelerated gradient-based iterative algorithm for solving extended Sylvester–conjugate matrix equations. The idea is from the gradient-based method introduced in Wu et al. ( Applied Mathematics and Computation 217(1): 130–142, 2010a) and the relaxed gradient-based algorithm proposed in Ramadan et al. ( Asian Journal of Control 16(5): 1–8, 2014) and the modified gradient-based algorithm proposed in Bayoumi (PhD thesis, Ain Shams University, 2014). The convergence analysis of the algorithm is investigated. We show that the iterative solution converges to the exact solution for any initial value provided some appropriate assumptions be made. A numerical example is given to illustrate the effectiveness of the proposed method and to test its efficiency and accuracy compared with an existing one presented in Wu et al. (2010a), Ramadan et al. (2014) and Bayoumi (2014).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.