Can We Improve the Standard Algorithm of Interval Computation by Taking Almost Monotonicity into Account?

Abstract

In many practical situations, it is necessary to perform interval computations – i.e., to find the range of a given function f(x1,…, xn) on given intervals – e.g., when we want to find guaranteed bounds of a quantity that is computed based on measurements, and for these measurements, we only have upper bounds of the measurement error. The standard algorithm for interval computations first checks for monotonicity. However, when the function f is almost monotonic, this algorithm does not utilize this fact. In this paper, we show that such closeness-to-monotonicity can be efficiently utilized.