论文标题
迭代方法
A barycentric trigonometric Hermite interpolant via an iterative approach
论文作者
论文摘要
在这项工作中，我们从满足Lagrange属性的基础功能开始构建一个Hermite interpolant。实际上，我们扩展并推广了Cirillo和Hormann（2018）引入的迭代方法，该方法为弗洛特·霍尔曼（Floater-Hormann）的插值家族。其次，我们将此方案应用于在一般订购的节点上产生有效的Barycentric三角赫尔米特插值，使用AS基础函数，由Berrut（1988）引入的三角插入术的函数。对于简单的计算结构，我们通过分析分析矩阵进行计算。最后，我们以各种示例和对等距节点和共形映射节点的收敛速率的数字研究得出结论。
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.
