The main aim of this paper intends to discuss the solution of fuzzy Sylvester matrix equation AX+XB=C where A= (aij)ÎRn´n, B= (bij) ÎRm´m are crisp M- matrices, C= (cij) ÎRn´m is fuzzy matrix and XÎRn´m is unknown, by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system to an (mn)´(mn) fuzzy system of linear equations. Then, we convert this system to three (mn)´(mn) crisp linear systems of equations, and we solve them simultaneously by ABS algorithm.

Solutions of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to con-struct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the given matrix. For this, an algorithm for constructing a general solution of the Sylvester matrix equation is used. The effectiveness of the proposed approaches is illustrated on the examples.

Global Krylov subspace methods are the most e cient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergence and symmetric positive defi nite splitting of the coe cient matrices. Convergence properties of this method are investigated. Finally, the e ectiveness of the nested splitting conjugate gradient method is explained by some numerical examples.

In this paper, we introduce two new schemes based on the global Hessen-berg processes for computing approximate solutions to low-rank Sylvester tensor equations. We first construct bases for the matrix and extended matrix Krylov subspaces by applying the global and extended global Hes-senberg processes. Then the initial problem is projected into the matrix or extended matrix Krylov subspaces with small dimensions. The reduced Sylvester tensor equation obtained by the projection methods can be solved by using a recursive blocked algorithm. Furthermore, we present the upper bounds for the residual tensors without requiring the computation of the approximate solutions in any iteration. Finally, we illustrate the perfor-mance of the proposed methods with some numerical examples.

In this paper, parametric Sylvester matrix equations whose elements are linear functions of interval parameters are considered. In contrast to deterministic problems, when a system of equations is derived from a stochastic model, its coefficients may depend on some parameters and so the parameterized system of equations appears. This work considers the parameterized Sylvester matrix equations and tries to propose some methods containing a direct method and two iterative methods to obtain outer estimations of the solution set.