Solution sets for systems of linear interval equations

Abstract

The paper discusses various classes of solution sets for linear interval systems of equations, and their properties. Interval methods constitute an important mathematical and computational tool for modelling real-world systems (especially mechanical) with (bounded) uncertainties of parameters, and for controlling rounding errors in computations. They are in principle much simpler than general probabilistic or fuzzy set formulation, while in the same time they conform very well with many practical situations. Linear interval systems constitute an important subclass of such interval models, still in the process of continuous development. Two important problems in this area are discussed in more detail- the classification of socalled united solution sets, and the problem of overestimation of interval enclosures (in the context of linear systems of equations called also a matrix coefficient dependence problem).