A barycentric trigonometric Hermite interpolant via an iterative approach

In this paper an interative approach for constructing the Hermite interpolant introduced by Cirillo and Hormann (2018) for the Floater-Hormann family of interpolants is extended and generalised. In particular, we apply that scheme to produce an effective barycentric rational trigonometric Hermite interpolant using the basis function of the interpolant introduced by Berrut (1988). In order to give an easy construction of such an interpolant we compute the differentation matrix analytically and we conclude with various examples and a numerical study of the rate of convergence at equidistant nodes.