On the Lebesgue constant of barycentric rational interpolation at equidistant nodes

Barycentric rational interpolation at quasi-equidistant nodes

A collection of recent papers reveals that linear barycentric rational interpolation with the weights suggested by Floater and Hormann is a good choice for approximating smooth functions, especially when the interpolation nodes are equidistant. In the latter setting, the Lebesgue constant of this rational interpolation process is known to grow only logarithmically with the number of nodes. But ...

A tighter upper bound on the Lebesgue constant of Berrut's rational interpolant at equidistant nodes

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results show tha...

Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points

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

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 satisfy a certain regularity condition, including Chebyshev–Gauss–Lobatto nodes as well as ex...

On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

We study the Lebesgue constant of the rational interpolant of Berrut (cf. [1]) when the interpolation points are equally distributed. In the more general case of the rational interpolant of Floater and Hormann (cf. [6]), we show by several numerical results, that the behavior of the Lebesgue constant on equally distributed points is consistent with that of Berrut’s interpolant.