论文标题
在枫树中混合
Blends in Maple
论文作者
论文摘要
对于单个变量的相同平滑的实地或复杂值函数的两个Taylor系列的混合物可用于近似。我们使用一个明确的公式用于两点Hermite插值多项式来构建此类混合物。我们展示了一种强大的枫木实现，可以使用线性成本的霍纳形式稳定有效地评估混合物，同时评估其衍生物为任意顺序，或者准确整合混合物。该实施适用于evalhf。我们为程序化使用提供顶级用户界面和有效的模块导出。这项工作是在2020年枫树会议上介绍的。请参见www.maplesoft.com/mapleconference
A blend of two Taylor series for the same smooth real- or complex-valued function of a single variable can be useful for approximation. We use an explicit formula for a two-point Hermite interpolational polynomial to construct such blends. We show a robust Maple implementation that can stably and efficiently evaluate blends using linear-cost Horner form, evaluate their derivatives to arbitrary order at the same time, or integrate a blend exactly. The implementation is suited for use with evalhf. We provide a top-level user interface and efficient module exports for programmatic use. This work was presented at the Maple Conference 2020. See www.maplesoft.com/mapleconference
