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A comparison of polynomial evaluation schemes

Laurent Fousse 1 Susanne Schmitt
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The goal of this paper is to analyze two polynomial evaluation schemes for multiple precision floating point arithmetic. Polynomials are used extensively in numerical computations (Taylor series for mathematical functions, root finding) but a rigorous bound of the error on the final result is seldom provided. We provide such an estimate for the two schemes and find how to reduce the number of operations required at run-time by a dynamic error analysis. This work is useful for floating point polynomial arithmetic.
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Conference papers
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https://hal.inria.fr/inria-00099918
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Submitted on : Tuesday, September 26, 2006 - 10:08:56 AM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM
Long-term archiving on: : Wednesday, March 29, 2017 - 1:11:30 PM

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  • HAL Id : inria-00099918, version 1

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Laurent Fousse, Susanne Schmitt. A comparison of polynomial evaluation schemes. 6th Conference on Real Numbers and Computers (RNC6), 2004, Dagstuhl, Germany, 17 p. ⟨inria-00099918⟩

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