Compensated Horner Scheme

Authors Philippe Langlois, Stef Graillat, Nicolas Louvet



PDF
Thumbnail PDF

File

DagSemProc.05391.3.pdf
  • Filesize: 255 kB
  • 29 pages

Document Identifiers

Author Details

Philippe Langlois
Stef Graillat
Nicolas Louvet

Cite AsGet 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

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail