Cheap and Tight Bounds on the Solution Set of Perturbed Systems of Nonlinear Equations

Abstract

This paper presents an iterative method for computing an outer interval bound on the solution set of parameters-dependent systems of non-linear equations for the case where the parameters take on their values within present intervals. The method is based on a recently suggested alternative linear interval enclosure of factorable non-linear functions in a given box. It comprises two stages: during the first stage, a relatively narrow starting box is determined using an appropriate inflation technique while the second stage aims at reducing the width of the starting box. Two algorithms implementing the method have been programmed in a C++ environment. Numerical examples seem to indicate that the second algorithm is rather efficient computation-wise. The method is self-validating: the fulfillment of a simple inclusion rule checked during its second stage ensures that the interval bound thus found is an outer approximation to the solution set of the perturbed system investigated.