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Roundoff errors for polynomial evaluation by a family of formulae

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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.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada/IUMA, University of Zaragoza, 50009, Zaragoza, Spain

    J. M. Carnicer & J. M. Peña

  2. Department of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

    T. N. T. Goodman

Authors
  1. J. M. Carnicer
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  2. T. N. T. Goodman
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  3. J. M. Peña
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Corresponding author

Correspondence to J. M. Carnicer.

Additional information

Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.

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Carnicer, J.M., Goodman, T.N.T. & Peña, J.M. Roundoff errors for polynomial evaluation by a family of formulae. Computing 82, 199–215 (2008). https://doi.org/10.1007/s00607-008-0007-6

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  • DOI: https://doi.org/10.1007/s00607-008-0007-6

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