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.
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Received December 14, 2001; revised March 27, 2002 Published online: July 8, 2002
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Ceberio, M., Granvilliers, L. Horner's Rule for Interval Evaluation Revisited. Computing 69, 51–81 (2002). https://doi.org/10.1007/s00607-002-1448-y
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DOI: https://doi.org/10.1007/s00607-002-1448-y
- AMS Subject Classifications: 12D10, 65G40.
- Keywords: Interval arithmetic, polynomial expression, interval evaluation, symbolic forms, factorization.