  This paper presents a novel set-based computing method, called interval
superposition arithmetic, for enclosing the image set of multivariate
factorable functions on a given domain. In order to construct such enclosures,
the proposed arithmetic operates over interval superposition models which are
parameterized by a matrix with interval components. Every point in the domain
of a factorable function is then associated with a sequence of components of
this matrix and the superposition, i.e. Minkowski sum, of these elements
encloses the image of the function at this point. Interval superposition
arithmetic has a linear runtime complexity with respect to the number of
variables. Besides presenting a detailed theoretical analysis of the accuracy
and convergence properties of interval superposition arithmetic, the paper
illustrates its advantages compared to existing set arithmetics via numerical
examples.
