Constrained Interval Arithmetic
Weldon Alexander Lodwick · 1999
: This paper presents an approach to solving the long-standing dependency problem in interval arithmetic. An extension to interval arithmetic, called here constrained interval arithmetic, is developed. Unlike interval arithmetic, constrained interval arithmetic has an additive inverse, a multiplicative inverse and satisfies the distributive law. This means that the algebraic structure of constrained interval arithmetic is different than that of interval arithmetic. The applicability of constrained interval arithmetic is explored. 1. Introduction: It is well-known in the interval analysis literature that interval arithmetic overestimates the resultant width of the interval when dependencies are present. This overestimation can be arbitrarily large (see, for example, (Neumaier 1990, pages 16-19)). Example 1Consider y = f(x) = x(1 \\Gamma x); x 2 [0; 1]: The implementation of interval arithmetic yields y = [0; 1] \\Theta (1 \\Gamma [0; 1]) = [0; 1] \\Theta [0; 1] = [0; 1]. The actual range...