Rounding Error Analysis for the Evaluation of a Polynomial and Some of Its Derivatives

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1974 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 11, pages 780-787 (issn: 0036-1429, eissn: 1095-7170,

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Authors: Wozniakowski, H.;

doi: 10.1137/0711064

Rounding Error Analysis for the Evaluation of a Polynomial and Some of Its Derivatives

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Abstract

We consider one-parameter family of Shaw–Traub algorithms (see [3]) for computing a polynomial and its normalized derivatives in floating point arithmetics fl, ${\text{fl}}_{\text{2}} $ and $\overline {{\text{fl}}} $. The numerical stability of this class is proved.

Keywords

Roundoff error, Numerical computation of solutions to single equations

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