# How can Newton's Divided Difference Interpolation accuracy be improved?

Are there any modifications to Newton's divided difference interpolation that can be made in order to improve the accuracy of the value given, specifically for exponential functions such as $y=e^{-x}-x$?

• Why do you need interpolation to compute $e^{-x}-x$? – Somos Feb 10 '18 at 13:17
• To find an estimation of its root without using original algebra methods. – Surely Advert Feb 10 '18 at 13:21
• To find the roots of $e^{-x}-x$ you need to compute the Lambert W function. – Somos Feb 10 '18 at 13:24