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Weighted interpolation for equidistant nodes

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Abstract

Weighted Lagrange interpolation is proposed for solving Lagrange interpolation problems on equidistant or almost equidistant data. Good condition numbers are found in the case of rational interpolants whose denominator has degree about twice the number of data to be interpolated. Since the degree of the denominator is higher than that of the numerator, simple functions like constants and linear polynomials will not be reproduced. Furthermore, the interpolant cannot be expressed by a barycentric formula. As a counterpart, the interpolation algorithm is simple and leads to small Lebesgue constants.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    Jesus M. Carnicer

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  1. Jesus M. Carnicer
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Correspondence to Jesus M. Carnicer.

Additional information

Partially supported by the Spanish Research Grant MTM2009-07315 and by Gobierno de Aragón.

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Carnicer, J.M. Weighted interpolation for equidistant nodes. Numer Algor 55, 223–232 (2010). https://doi.org/10.1007/s11075-010-9399-4

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  • DOI: https://doi.org/10.1007/s11075-010-9399-4

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