A barycentric trigonometric Hermite interpolant via an iterative approach

In this work we extend and generalise an iterative approach, introduced by Cirillo and Hormann (2018) for the Floater-Hormann family of interpolants, to construct an Hermite interpolant for general interpolant with basis functions which satisfy a Lagrange property. In particular, we apply this scheme to produce an effective barycentric rational trigonometric Hermite interpolant using the basis functions of the trigonometric interpolant introduced by Berrut (1988). Moreover, in order to give an easy construction of such an interpolant we compute analytically the differentation matrix and we conclude with various examples and a numerical study of the rate of convergence at equidistant nodes.