Verification and Practice on Forward-Difference Based First-Order Numerical-Differentiation Formulas

Based on the polynomial-interpolation theory,interpolating polynomials could be constructed to approximate an unknown target-function.Then,the first-order numerical-differentiation formulas could be obtained by differentiating the constructed interpolating polynomials.This paper investigates the approximate first-order numerical-differentiation formulas of the unknown target-function in terms of multiple sampling-nodes by using the forward-difference method.Specifically,the equally-spaced forward-difference formulas involving two to sixteen sampling-nodes are presented.Computer experimental results verify and show that relatively high computational precision could be achieved by using the presented formulas to estimate the numerical values of the first-order derivatives of unknown target-functions.