Modified Affine Arithmetic Is More Accurate than Centered Interval Arithmetic or Affine Arithmetic

In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard a#ne arithmetic, and (ii) modified a#ne arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified a#ne arithmetic is not only more accurate but also much faster than standard a#ne arithmetic. We thus suggest that modified a#ne arithmetic is the method of choice for evaluating algebraic functions, such as implicit surfaces, over a box