Lagrange interpolation to compute the derivatives of a function

摘要

Recently efforts have been made to quantify the difficulties in numerically to compute the derivative of a function [Computing Methods, Pergamon Press, Oxford, vol. 1, 1965; Comput. Math. Appl. 19 (5) (1990) 1; Numerical Analysis, Wiley, New York, 1955]. The only disadvantage of approximation by Chebyshev polynomials lies in the fact that the abscissas xi cannot be chosen freely. On other hand, Lagrange interpolation is suitable to use with equal or nonequal step. This paper describes a method to compute the first or the second derivative of a function. The method is tested by different examples.