Parametric AE-solution sets to the parametric linear systems with multiple right-hand sides and parametric matrix equation A( p) X = B( p).

In this paper, the parametric matrix equation A( p) X = B( p) whose elements are linear functions of uncertain parameters varying within intervals are considered. In this matrix equation A( p) and B( p) are known m-by- m and m-by- n matrices respectively, and X is the m-by- n unknown matrix. We discuss the so-called AE-solution sets for such systems and give some analytical characterizations for the AE-solution sets and a sufficient condition under which these solution sets are bounded. We then propose a modification of Krawczyk operator for parametric systems which causes reduction of the computational complexity of obtaining an outer estimation for the parametric united solution set, considerably. Then we give a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for enclosing the parametric united solution set which also enables us to reduce the computational complexity, significantly. Also some numerical approaches based on Gaussian elimination and Gauss-Seidel methods to find outer estimations for the parametric united solution set are given. Finally, some numerical experiments are given to illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]