通过求解适当的微分方程确定Hermite插值逼近中的Rolle函数
Determining the Rolle function in Hermite interpolatory approximation by solving an appropriate differential equation
Mathsophical Ltd.（Mathsophical有限公司）
AI总结：
本文通过求解适当的微分方程确定Hermite插值的误差项，利用多项式近似误差项来提高插值精度，并通过实例展示精度提升的效果。
摘要：
我们通过数值求解由误差项本身导出的适当微分方程来确定Hermite插值的点误差。我们利用这一知识通过多项式近似误差项，并将其加到原始Hermite多项式上以形成更精确的近似。一个例子显示了精度的显著改进。
英文摘要：
We determine the pointwise error in Hermite interpolation by numerically solving an appropriate differential equation, derived from the error term itself. We use this knowledge to approximate the error term by means of a polynomial, which is then added to the original Hermite polynomial to form a more accurate approximation. An example demonstrates that improvements in accuracy are significant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
