通过确定余项提高泰勒多项式的精度
Enhancing the accuracy of the Taylor polynomial by determining the remainder term
摘要：
我们通过求解一个适当的初值问题来确定Taylor多项式逼近中的Lagrange函数。因此，我们确定余项，然后通过自然的三次样条近似。这导致泰勒近似的质量显著提高。我们观察到改进的精度的近似的许多数量级，包括一个情况下，当自变量x超出相关的收敛半径。
英文摘要：
We determine the Lagrange function in Taylor polynomial approximation by solving an appropriate initial-value problem. Hence, we determine the remainder term which we then approximate by means of a natural cubic spline. This results in a significant improvement in the quality of the Taylor approximation. We observe improvements in the accuracy of the approximation of many orders of magnitude, including a case when the independent variable x lies beyond the relevant radius of convergence.
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。
