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

Wolfgang Erb

Applied Mathematics and Computation, 2016, vol. 289, issue C, 409-425

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.

Keywords: Bivariate Lagrange interpolation; Chebyshev lattices; Lissajous curves; Padua points; Quadrature formulas (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:289:y:2016:i:c:p:409-425

DOI: 10.1016/j.amc.2016.05.019

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