Generalized solution sets of the interval generalized Sylvester matrix equation ∑i=1pAiXi+∑j=1qYjBj=C and some approaches for inner and outer estimations

In this work, we extend the concept of generalized solution sets that is introduced for the first time by Shary (1996, 1999), to the interval generalized Sylvester matrix equation ∑i=1pAiXi+∑j=1qYjBj=C. Then AE-solution sets for this equation will be characterized and we develop some approaches (called algebraic approaches) in which the inner and outer estimation problems for some special cases of AE-solution sets reduce to problems of computing algebraic solutions of some auxiliary interval equations. Also we present a numerical technique that is an extension of the well-known interval Gauss–Seidel method for outer estimation of the solution set.