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Running Error Analysis of Evaluation Algorithms for Bivariate Polynomials in Barycentric Bernstein Form

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Abstract

Running error analysis for the bivariate de Casteljau algorithm and the VS algorithm is performed. Theoretical results joint with numerical experiments show the better stability properties of the de Casteljau algorithm for the evaluation of bivariate polynomials defined on a triangle in spite of the lower complexity of the VS algorithm. The sharpness of our running error bounds is shown.

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Authors and Affiliations

  1. Dept. Mathematica, Universidad de Cantabria, Avenida. de los Castros s/n, 39005, Santander, Spain

    E. Mainar

  2. Universidad de Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

    J. M. Peña

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  1. E. Mainar
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  2. J. M. Peña
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Correspondence to E. Mainar.

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Mainar, E., Peña, J.M. Running Error Analysis of Evaluation Algorithms for Bivariate Polynomials in Barycentric Bernstein Form. Computing 77, 97–111 (2006). https://doi.org/10.1007/s00607-005-0149-8

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  • DOI: https://doi.org/10.1007/s00607-005-0149-8

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