A Haskell implementation of the Lyness-Moler’s numerical differentiation algorithm

Abstract

This paper describes a computational problem encountered in numerical differentiation. By restricting the problem to a proper subclass of differentiable functions, a numerical solution first proposed by Lyness and Moler is considered and implemented in the functional programming language Haskell. The accuracy of the calculation of the numerical derivative using the Lyness-Moler's method crucially lies in our recursive algorithm for computing contour integrals.