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

Peter Dencker; Wolfgang Erb; Yurii Kolomoitsev; Tetiana Lomako

doi:10.1016/j.jco.2017.05.001

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

Institute of Mathematics

12 Citations (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 language	English
Journal	Journal of Complexity
Volume	43
Pages (from-to)	1-27
Number of pages	27
ISSN	0885-064X
DOIs	https://doi.org/10.1016/j.jco.2017.05.001
Publication status	Published - 01.12.2017

Funding

Wolfgang Erb was supported by the German Research Foundation (DFG, grant number ER 777/1-1). Yurii Kolomoitsev and Tetiana Lomako was supported by H2020-MSCA-RISE-2014 Project number 645672.

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10.1016/j.jco.2017.05.001

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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.",

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AU - Dencker, Peter

AU - Erb, Wolfgang

AU - Kolomoitsev, Yurii

AU - Lomako, Tetiana

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85020630990

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M3 - Journal articles

AN - SCOPUS:85020630990

SN - 0885-064X

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SP - 1

EP - 27

JO - Journal of Complexity

JF - Journal of Complexity

ER -

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

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