Automatic Computation of a Linear Interval Enclosure

Recently, an alternative interval approximation F X ( ) for enclosing a factorable function f(x) in a given box X has been suggested. The enclosure is in the form of an affine interval function F X a X B i i i n ( ) = + ∑ =1 where only the additive term B is an interval, the coefficients ai being real numbers. The approximation is applicable to continuously differentiable, continuous and even discontinuous functions. In this paper, a new algorithm for determining the coefficients ai and the interval B of F(X) is proposed. It is based on the introduction of a specific generalized representation of intervals which permits the computation of the enclosure considered to be fully automated.