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Accurate polynomial interpolation by using the Bernstein basis

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Abstract

The problem of polynomial interpolation with the Lagrange-type data when using the Bernstein basis instead of the monomial basis is addressed. The extension to the bivariate case, which leads to the use of a generalized Kronecker product, is also developed. In addition to the matricial description of the solution and the proof of unisolvence, algorithms for the computation of the coefficients of the interpolating polynomial are presented. Numerical experiments illustrating the advantage of computing with Bernstein-Vandermonde matrices instead of with Vandermonde matrices are included.

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Authors and Affiliations

  1. Departamento de Física y Matemáticas, Universidad de Alcalá, Campus Universitario, 28871, Alcalá de Henares (Madrid), Spain

    Ana Marco, José-Javier Martínez & Raquel Viana

Authors
  1. Ana Marco
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  2. José-Javier Martínez
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  3. Raquel Viana
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Corresponding author

Correspondence to José-Javier Martínez.

Additional information

Dedicated to Mariano Gasca and Günter Mühlbach

This research has been partially supported by the Spanish Research Grant MTM2015-65433-P (MINECO/FEDER) from the Spanish Ministerio de Economía y Competitividad.

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Marco, A., Martínez, JJ. & Viana, R. Accurate polynomial interpolation by using the Bernstein basis. Numer Algor 75, 655–674 (2017). https://doi.org/10.1007/s11075-016-0215-7

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