Roundoff errors for polynomial evaluation by a family of formulae

Authors:
J. M. Carnicer;T. N. T. Goodman;J. M. Peña
Affiliations:
University of Zaragoza, Departamento de Matemática Aplicada/IUMA, 50009, Zaragoza, Spain;University of Dundee, Department of Mathematics, DD1 4HN, Dundee, UK;University of Zaragoza, Departamento de Matemática Aplicada/IUMA, 50009, Zaragoza, Spain
Venue:
Computing
Year:
2008

Citing 5
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Abstract

A roundoff error analysis of formulae for evaluating polynomials is performed. The considered formulae are linear combinations of basis functions, which can be computed with high relative accuracy. We have taken into account that all steps but the last one can be computed to high relative accuracy. The exactness of the initial data is crucial for obtaining low error bounds. The Lagrange interpolation formula and related formulae are considered and numerical experiments are provided.