In this work we construct an Hermite interpolant starting from basis functions that satisfy a Lagrange property. In fact, we extend and generalise an iterative approach, introduced by Cirillo and Hormann (2018) for the Floater-Hormann family of interpolants. Secondly, we apply this scheme to produce an effective barycentric rational trigonometric Hermite interpolant at general ordered nodes using as basis functions the ones of the trigonometric interpolant introduced by Berrut (1988). For an easy computational construction, we calculate analytically the differentation matrix. Finally, we conclude with various examples and a numerical study of the rate of convergence at equidistant nodes and conformally mapped nodes.

翻译：本文从满足Lagrange性质的基函数出发，构造了一种Hermite插值函数。具体而言，我们扩展并推广了Cirillo与Hormann（2018）针对Floater-Hormann插值族提出的迭代方法。其次，我们将该方案应用于一般有序节点，以Berrut（1988）提出的三角插值基函数为基础，构建了一种有效的重心有理三角Hermite插值函数。为便于计算实现，我们解析推导了微分矩阵。最后，通过多种算例及等距节点与共形映射节点收敛速率的数值研究，对方法进行了总结分析。