A Limitation for Underestimation via Twin Arithmetic

摘要

Computing an enclosure for the range of a rational function over an interval is one of the main goals of interval analysis. One way to obtain such an enclosure is to use interval arithmetic evaluation of a formula for the function. Often one would like to check how close the overestimation is to the correct range. Kreinovich, Nesterov, and Zheludeva (Reliable Computing 2 (2) (1996)) suggested a new kind of twin arithmetic which produces a twin of intervals at the same time: the usual enclosure, i.e. an interval which is an overestimation for the range, and an interval which is contained in the range, i.e. an interval which is an underestimation for the range.