On the Lebesgue constant for the Xu interpolation formula

Authors:
Len Bos;Stefano De Marchi;Marco Vianello
Affiliations:
Department of Mathematics and Statistics, University of Calgary, Canada;Department of Computer Science, University of Verona, Verona, Italy;Department of Pure and Applied Mathematics, University of Padova, Italy
Venue:
Journal of Approximation Theory
Year:
2006

Citing 2
Cited 6

Lagrange interpolation on Chebyshev points of two variables

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A Numerical Study of the Xu Polynomial Interpolation Formula in Two Variables

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Hyperinterpolation in the cube

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On multivariate projection operators

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Full length article: Minimal cubature rules and polynomial interpolation in two variables

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Radial orthogonality and Lebesgue constants on the disk

Numerical Algorithms

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Abstract

In the paper [Y. Xu, Lagrange interpolation on Chebyshev points of two variables, J. Approx. Theory 87 (1996) 220-238], the author introduced a set of Chebyshev-like points for polynomial interpolation (by a certain subspace of polynomials) in the square [-1, 1]2, and derived a compact form of the corresponding Lagrange interpolation formula. In [L. Bos, M. Caliari, S. De Marchi, M. Vianello, A numerical study of the Xu polynomial interpolation formula in two variables, Computing 76(3-4) (2005) 311-324], we gave an efficient implementation of the Xu interpolation formula and we studied numerically its Lebesgue constant, giving evidence that it grows like O((log n)2), n being the degree. The aim of the present paper is to provide an analytic proof to show that the Lebesgue constant does have this order of growth.