Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next?

In interval computations, the range of each intermediate result r is described by an interval r. To decrease excess interval width, we can keep some information on how r depends on the input x=(x1,...,xn). There are several successful methods of approximating this dependence; in these methods, the dependence is approximated by linear functions (affine arithmetic) or by general polynomials (Taylor series methods). Why linear functions and …