Horner's rule for interval evaluation revisited

  • Authors:

  • M. Ceberio;L. Granvilliers

  • Affiliations:

  • IRIN -- Université de Nants B.P. 92208 -- 44322 Nantes Cedex 3 -- France;IRIN -- Université de Nants B.P. 92208 -- 44322 Nantes Cedex 3 -- France

  • Venue:
  • Computing
  • Year:
  • 2002

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Abstract

Interval arithmetic can be used to enclose the range of a real function over a domain. However, due to some weak properties of interval arithmetic, a computed interval can be much larger than the exact range. This phenomenon is called dependency problem. In this paper, Horner's rule for polynomial interval evaluation is revisited. We introduce a new factorization scheme based on well-known symbolic identities in order to handle the dependency problem of interval arithmetic. The experimental results show an improvement of 25% of the width of computed intervals with respect to Horner's rule.