Interval Superposition Arithmetic

This paper presents a novel set-based computing method, called intervalsuperposition arithmetic, for enclosing the image set of multivariatefactorable functions on a given domain. In order to construct such enclosures,the proposed arithmetic operates over interval superposition models which areparameterized by a matrix with interval components. Every point in the domainof a factorable function is then associated with a sequence of components ofthis matrix and the superposition, i.e. Minkowski sum, of these elementsencloses the image of the function at this point. Interval superpositionarithmetic has a linear runtime complexity with respect to the number ofvariables. Besides presenting a detailed theoretical analysis of the accuracyand convergence properties of interval superposition arithmetic, the paperillustrates its advantages compared to existing set arithmetics via numericalexamples.