Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous–Chebyshev nodes

Peter Dencker, Wolfgang Erb, Yurii Kolomoitsev*, Tetiana Lomako

*Corresponding author for this work
1 Citation (Scopus)

Abstract

To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous–Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue constant. The proof is based on a relation between the Lebesgue constant for the polynomial interpolation problem and the Lebesgue constant linked to the polyhedral partial sums of Fourier series. The magnitude of the obtained bounds is determined by a product of logarithms of the side lengths of the considered polyhedral sets and shows the same behavior as the magnitude of the Lebesgue constant for polynomial interpolation on the tensor product Chebyshev grid.

Original languageEnglish
JournalJournal of Complexity
Volume43
Pages (from-to)1-27
Number of pages27
ISSN0885-064X
DOIs
Publication statusPublished - 01.12.2017

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