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MPI-I-2004-1-005

A comparison of polynomial evaluation schemes

Schmitt, Susanne and Fousse, Laurent

MPI-I-2004-1-005. June 2004, 19 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
The goal of this paper is to analyze two polynomial evaluation
schemes (naive and Horner method) for multiprecision 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
multiprecision floating point evaluation of truncated power series.

Acknowledgement:
References to related material:

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Hide details for BibTeXBibTeX
@TECHREPORT{SchmittFoussee2004,
  AUTHOR = {Schmitt, Susanne and Fousse, Laurent},
  TITLE = {A comparison of polynomial evaluation schemes},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2004-1-005},
  MONTH = {June},
  YEAR = {2004},
  ISSN = {0946-011X},
}