An improved numerical approximation for the first derivative

Abstract

The traditional numerical computation of the first derivative f '(x) of a given function f (x) of a single argument x by central differencing is known to involve aspects of both accuracy and precision. By analysing both we arrive at an algorithm that closely approximates the most accurate answer obtainable by this method, typically with at least 9 accurate decimals, while preserving a minimal footprint. The results apply to software based on the IEEE-754 specification, and are illustrated with Excel. © Indian Academy of Sciences.