“Even with THAT Step Size?”

Abstract

SummaryThe centered difference quotient is the simplest centered approximation for the derivative of a function at a point. In this paper, we explore and apply general centered approximation formulae for the derivative of a function at a point using any number of weighted evenly-spaced nodes. The resulting formulae have connections to both Vandermonde matrices and Lagrange polynomials and lead to interesting combinatorial identities.