In the paper \cite{xu3}, 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 \cite{nostro1} we gave an efficient implementation of the Xu interpolation formula and we studied numerically the Lebesgue constant of the Xu points, giving evidence that it grows like ${\cal O}((\log n)^2)$, $n$ being the degree. The aim of the present paper is to provide an analytic proof that indeed the Lebesgue constant does have this order of growth.
The Lebesgue constant of the Xu interpolation points
L. Bos;DE MARCHI, Stefano;
2006-01-01
Abstract
In the paper \cite{xu3}, 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 \cite{nostro1} we gave an efficient implementation of the Xu interpolation formula and we studied numerically the Lebesgue constant of the Xu points, giving evidence that it grows like ${\cal O}((\log n)^2)$, $n$ being the degree. The aim of the present paper is to provide an analytic proof that indeed the Lebesgue constant does have this order of growth.
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