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.

翻译：本文推广并泛化了Cirillo与Hormann（2018）针对Floater-Hormann插值函数族提出的迭代方法，以构造满足Lagrange性质的基函数所对应的Hermite插值函数。具体而言，我们利用Berrut（1988）提出的三角插值基函数，将此方案应用于构建有效的重心有理三角Hermite插值函数。此外，为简化该插值函数的构造过程，我们解析计算了微分矩阵，并通过多种实例及等距节点收敛速率的数值研究加以验证。