Interval Superposition Arithmetic
Abstract
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.
Cite
@article{arxiv.1610.05862,
title = {Interval Superposition Arithmetic},
author = {Yanlin Zha and Mario E. Villanueva and Boris Houska},
journal= {arXiv preprint arXiv:1610.05862},
year = {2018}
}