Computation of Integrals of Uncertain Vector Functions

The paper deals with the problem of numerical integration of a function [0, 1]→ R for which only a set-membership description is known. The set of values of the integrals of all possible realizations of the uncertain function is considered as a guaranteed result of the integration. The problem is to approximate this set, with a prescribed accuracy ε, by polyhedral sets, in particular, to enclose it in an n-dimensional interval which is ε-minimal. In the first part of the paper we focus on quadrature formulae for set-valued integrals and the estimation of their errors. In the second part we sketch the idea of their implementation.