It has recently been shown that the Lebesgue constant for Berrut’s rational interpolant at equidistant nodes grows logarithmically in the number of interpolation nodes. In this paper we show that the same holds for a very general class of well-spaced nodes and essentially any distribution of nodes that satisfies a certain regularity condition, including Chebyshev–Gauss–Lobatto nodes as well as extended Chebyshev nodes.
Bounding the Lebesgue constant of Berrut's rational interpolant at general nodes
DE MARCHI, STEFANO;
2013
Abstract
It has recently been shown that the Lebesgue constant for Berrut’s rational interpolant at equidistant nodes grows logarithmically in the number of interpolation nodes. In this paper we show that the same holds for a very general class of well-spaced nodes and essentially any distribution of nodes that satisfies a certain regularity condition, including Chebyshev–Gauss–Lobatto nodes as well as extended Chebyshev nodes.File in questo prodotto:
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