#### Publication Date

6-2017

#### Abstract

One of the main problem of interval computations is computing the range of a given function over given intervals. It is known that naive interval computations always provide an enclosure for the desired range. Sometimes -- e.g., for single use expressions -- naive interval computations compute the exact range. Sometimes, we do not get the exact range when we apply naive interval computations to the original expression, but we get the exact range if we apply naive interval computations to an equivalent reformulation of the original expression. For some other functions -- including some polynomials -- we do not get the exact range no matter how we reformulate the original expression. In this paper, we are looking for the simplest of such polynomials -- simplest in several reasonable senses: that it depends on the smallest possible number of variables, that it has the smallest possible number of monomials, that it has the smallest degree, etc. We then prove that among all polynomials for which naive interval computations cannot be exact, there exists a polynomial which is the simplest in all these senses.

## Comments

Technical Report: UTEP-CS-17-58