Barycentric rational interpolation at quasi-equidistant nodes

On the Lebesgue constant of barycentric rational interpolation at equidistant nodes

Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and importan...

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

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...

The Linear Barycentric Rational Quadrature Method for Volterra

We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate as the rational quadrature rule but is costly on long integration intervals. The second, based on a co...

Exponential convergence of a linear rational interpolant between transformed Chebyshev points

In 1988 the second author presented experimentally well-conditioned linear rational functions for global interpolation. We give here arrays of nodes for which one of these interpolants converges exponentially for analytic functions Introduction Let f be a complex function defined on an interval I of the real axis and let x0, x1, . . . , xn be n + 1 distinct points of I, which we do not assume e...