A Linear Complementarity Problem with a P-Matrix

Abstract

In this paper, we present an application of a linear complementarity problem where M is a P-matrix but, in general, is neither an H-matrix nor a positive definite matrix. This application occurs originally in [J. Rohn, Linear Algebra Appl., 126 (1989), pp. 39--78], which is less known to the LCP community. Its focus is in computing the exact interval enclosures of the components of the solution set of an interval linear system. We extend the idea such that the calculations can be done by a computer with rigorous error control.