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Asymptotics of the Lebesgue constants for bivariate approximation processes

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  • Kolomoitsev, Yurii
  • Lomako, Tetiana

Abstract

In this paper asymptotic formulas are given for the Lebesgue constants generated by three special approximation processes related to the ℓ1-partial sums of Fourier series. In particular, we consider the Lagrange interpolation polynomials based on the Lissajous-Chebyshev node points, the partial sums of the Fourier series generated by the anisotropically dilated rhombus, and the corresponding discrete partial sums.

Suggested Citation

  • Kolomoitsev, Yurii & Lomako, Tetiana, 2021. "Asymptotics of the Lebesgue constants for bivariate approximation processes," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    • Handle: RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300321002824
    DOI: 10.1016/j.amc.2021.126192
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    References listed on IDEAS

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    1. 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.
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