Parameterized outer estimation of AE-solution sets to parametric interval linear systems

Abstract

We consider linear algebraic equations, where the elements of the matrix and of the right-hand side vector are linear functions of interval parameters, and their parametric AE-solution sets, which are defined by applying universal and existential quantifiers to the interval parameters. Usually, interval methods find numerical interval vector that contains an AE-solution set.In this work we propose a method that generates an outer estimate of a parametric AE-solution set in form of a linear parametric interval function, called parameterized outer solution (p-solution). Parameterized outer solution is proposed for the parametric united solution set in Kolev (2014) and takes precedence over the classical interval solution enclosure when the latter is part of other problems involving the same parameters. The method we present generalizes the method from Kolev (2016) for parametric AE-solution sets. It is also a parameterized analogue of a method from Popova and Hladík (2013) and produces the same interval enclosure as the method from the last reference.