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A comparison of polynomial evaluation schemes

Schmitt, Susanne and Fousse, Laurent

June 2004, 19 pages.

Status: available - back from printing

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.

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  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},