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Mathematics > Numerical Analysis

arXiv:1503.00895 (math)
[Submitted on 3 Mar 2015 (v1), last revised 3 Apr 2016 (this version, v2)]

Title:Bivariate Lagrange interpolation at the node points of Lissajous curves - the degenerate case

Authors:Wolfgang Erb
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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.
Comments: 26 pages, 6 figures, 1 table
Subjects: Numerical Analysis (math.NA)
MSC classes: 33C50, 41A05, 65D05
Cite as: arXiv:1503.00895 [math.NA]
  (or arXiv:1503.00895v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1503.00895

Submission history

From: Wolfgang Erb [view email]
[v1] Tue, 3 Mar 2015 11:00:13 UTC (1,012 KB)
[v2] Sun, 3 Apr 2016 16:54:11 UTC (1,041 KB)
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