Estimation of algebraic solution by limiting the solution set of an interval linear system

In this paper, we introduce a new method for estimating the algebraic solution of an interval linear system (ILS) whose coefficient matrix is real-valued and righthand side vector is interval-valued. In the proposed method, we first apply the interval Gaussian elimination procedure to obtain the solution set of an interval linear system and then by limiting the solution set of related ILS by the limiting factors, we get an algebraic solution of ILS. In addition, we prove that the obtained solution by our method satisfies the related interval linear system. Finally, based on our method, an algorithm is proposed and numerically demonstrated.