Iterative methods for enclosing the solution set of the parametric Sylvester matrix equation

In this paper, we study the parametric Sylvester matrix equation A(p)X+XB(p)=C(p) whose elements are linear functions of some parameters varying within intervals. We first present some characterizations of its solution set and then using these characterizations, we give some sufficient conditions for boundedness of the solution set. We then propose two efficient iterative methods to find some enclosures to the solution set. The introduced iterative methods reduce the computational costs of enclosing the solution set of our problem with respect to the other methods, considerably. Finally, by some numerical methods we show the effectiveness of the proposed methods.