Elsevier

Journal of Complexity

Volume 43, December 2017, Pages 1-27
Journal of Complexity

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

https://doi.org/10.1016/j.jco.2017.05.001Get rights and content
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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.

Keywords

Interpolation
Lissajous–Chebyshev nodes
Lebesgue constants
Polyhedra

Cited by (0)

Communicated by A. Hinrichs.