Compensated Horner Scheme

Langlois, Philippe; Graillat, Stef; Louvet, Nicolas

doi:10.4230/DagSemProc.05391.3

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Compensated Horner Scheme

Authors Philippe Langlois, Stef Graillat, Nicolas Louvet

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 5391
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2006-01-31

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Document Identifiers

DOI: 10.4230/DagSemProc.05391.3
URN: urn:nbn:de:0030-drops-4423

Subject Classification

Keywords

Polynomial evaluation
Horner scheme
error-free transformation
floating point arithmetic
accuracy

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Abstract

Using error-free transformations, we improve the classic Horner Scheme (HS)
to evaluate (univariate) polynomials in floating point arithmetic. 
We prove that this Compensated Horner Scheme (CHS) is as accurate as HS
performed with twice the working precision. 
Theoretical analysis and experiments exhibit a reasonable running time
overhead being also more interesting than double-double implementations. 
We introduce a dynamic and validated error bound of the CHS computed value.

The talk presents these results together with a survey about error-free
transformations and related hypothesis.

Cite As Get BibTex

Philippe Langlois, Stef Graillat, and Nicolas Louvet. Compensated Horner Scheme. In Algebraic and Numerical Algorithms and Computer-assisted Proofs. Dagstuhl Seminar Proceedings, Volume 5391, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006) https://doi.org/10.4230/DagSemProc.05391.3

Author Details

Philippe Langlois

Stef Graillat

Nicolas Louvet

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