An application of generalized absolute value equation

In this paper, an application of the generalized absolute value equation is exploited. Concretely, by using the generalized absolute value equation, we provide a new approach to efficiently obtain the hull of the solution set to interval linear equations with certain inverse positive coefficient interval matrix. Compared with some existed classical methods such as the magnitude method, Krawczyk method, the interval Gauss-Seidel method, and sign accord algorithm, in the implementations, this new approach only requires finding the solutions of two absolute value equations, which only involves the matrix-vector multiplication, and avoids the complex interval-matrix-vector multiplication. To make sure that the proposed method is convergent, some convergence conditions are presented. To confirm the performance of the proposed method, some numerical examples are provided.