In the talk we summarize the results recently obtained on the study of the Lebesgue constants of the family of Floater-Hormann Rational Interpolants (FHRI) both on equispaced [1] and quasi-equispaced points [2]. If time allows, we shall also discuss on a Matlab package that implements the FHRI and some of its "natural" applications to quadrature and least-squares.
References:
[1] L. Bos, S. De Marchi, K. Hormann and G. Klein: On the Lebesgue constant of barycentric rational interpolation at equidistant nodes, Numer. Math. 121(3) 2012, 461-471
[2] K. Hormann, G. Klein and S. De Marchi: Barycentric rational interpolation at quasi-equidistant nodes, Dolomites Res. Notes Approx, Vol 5, 2012, pp. 1-6