一种用于埃尔米特插值的直接方法
A Direct Approach to Hermite Interpolation
AI总结：
该研究引入一族满足埃尔米特插值自然对偶关系的多项式，给出任意重数埃尔米特插值的显式公式，无需差商等。还阐述了埃尔米特基于积分公式的原始方法，包括推导插值多项式及估计全纯数据插值误差。
AI中文摘要：
我们引入了一族满足埃尔米特插值自然对偶关系的多项式，类似于经典拉格朗日插值多项式。它们给出了具有任意重数的埃尔米特插值的显式封闭公式，无需借助差商、递归修正或辅助贝祖等式。我们还详细阐述了埃尔米特基于积分公式的原始方法，他用此推导插值多项式并估计全纯数据的插值误差。
英文摘要：
We introduce a family of polynomials satisfying the natural duality relations for Hermite interpolation, analogous to the classical Lagrange interpolation polynomials. They yield an explicit closed formula for the Hermite interpolant with arbitrary multiplicities, without recourse to divided differences, recursive corrections, or auxiliary Bézout identities. We also give a detailed account of Hermite's original approach to the problem, based on an integral formula, which he used both to derive the interpolating polynomial and to estimate the interpolation error for holomorphic data.
