Verification and Practice on First-Order Numerical Differentiation Formulas for Unknown Target Functions

Abstract

Based on the polynomial-interpolation theory,the Lagrange interpolating polynomial could be constructed by using the corresponding discrete-time values of an unknown target-function.Then,the approximate first-order numerical-differentiation formulas could be derived in terms of those multiple sampling-nodes.Hence,the equally-spaced backward-difference formulas involving two to sixteen sampling-nodes.Experimental results verify that the relatively high computational-precision could be achieved by using these formulas,when estimating the numerical values of the first-order derivative of unknown target-functions are estimated.