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.

翻译：我们通过用数字方法解决一个从错误名本身产生的适当的差分方程来确定Hermite内插的点误差。 我们用这一知识用一个多义来估计错误词,然后将其添加到原Hermite多义中,以形成一个更准确的近似值。 一个例子表明精确度的提高是显著的。</s>