|Given the function f(x), compute dn f/dxn at given x|
Numerical differentiation deals with the following problem: We are given the function y = f(x) and wish to obtain one of its derivatives at the point x = xk. The term “given” means that we either have an algorithm for computing the function, or we possess a set of discrete data points (xi,yi), i = 0, 1, …, n. In either case, we have access to a finite number of (x,y) data pairs from which to compute the derivative. If you suspect by now that numerical differentiation is related to interpolation, you are correct—one means of finding the derivative is to approximate the function locally by a polynomial and then to differentiate it. An ...