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Bivariate Lagrange interpolation at the node points of Lissajous curves – the degenerate case

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  • Erb, Wolfgang

Abstract

In this article, we study bivariate polynomial interpolation on the node points of degenerate Lissajous figures. These node points form Chebyshev lattices of rank 1 and are generalizations of the well-known Padua points. We show that these node points allow unique interpolation in appropriately defined spaces of polynomials and give explicit formulas for the Lagrange basis polynomials. Further, we prove mean and uniform convergence of the interpolating schemes. For the uniform convergence the growth of the Lebesgue constant has to be taken into consideration. It turns out that this growth is of logarithmic nature.

Suggested Citation

  • Erb, Wolfgang, 2016. "Bivariate Lagrange interpolation at the node points of Lissajous curves – the degenerate case," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 409-425.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:409-425
    DOI: 10.1016/j.amc.2016.05.019
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    Cited by:

    1. De Marchi, S. & Marchetti, F. & Perracchione, E. & Poggiali, D., 2021. "Multivariate approximation at fake nodes," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Kolomoitsev, Yurii & Lomako, Tetiana, 2021. "Asymptotics of the Lebesgue constants for bivariate approximation processes," Applied Mathematics and Computation, Elsevier, vol. 403(C).

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