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
翻译:将两个泰勒系列混合为同一变量的平滑、实际或复杂估价的功能组合成两个泰勒系列,对于近似可能有用。我们用一个明确的公式来构造这种混合。我们用一个两点的赫米特间多极性混合公式来构建这种混合。我们展示了一种强有力的“地图”实施方式,它能够用线性成本角形对混合进行评估,同时评价其衍生物达到任意秩序,或者完全结合混合。执行适合与evalhf一起使用。我们为方案使用提供了一个顶级用户界面和高效模块出口。这项工作在2020年的马普勒会议上作了介绍。见www.mapleoft.com/mapleconference。