Bounding the Lebesgue constant for Berrut’s rational interpolant at general nodes

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.