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

  • Huahao Shou
  • Hongwei Lin
  • Ralph Martin
  • Guojin Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2768)

Abstract

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 affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not only more accurate but also much faster than standard affine arithmetic. We thus suggest that modified affine arithmetic is the method of choice for evaluating algebraic functions, such as implicit surfaces, over a box.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Huahao Shou
    • 1
    • 2
  • Hongwei Lin
    • 1
  • Ralph Martin
    • 3
  • Guojin Wang
    • 1
  1. 1.State Key Laboratory of CAD & CGZhejiang UniversityHangzhouChina
  2. 2.Department of Applied MathematicsZhejiang University of TechnologyHangzhouChina
  3. 3.Department of Computer ScienceCardiff UniversityCardiffUK

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