Precise calculation of numerical derivatives using Lagrange and Hermite interpolation (Q918621)

The author derives formulae based on the classical Lagrange and Hermite interpolation. Lagrange interpolation is used when the function is given at equidistant nodes and one wants the values of the derivatives at these nodes. Hermite interpolation is used when the data contains values of some derivatives at some nodes. Practically, the expressions for the derivatives from the Lagrange and Hermite interpolation formulae become very cumbersome when the number of nodes increases. For this reason, the author exploits these general expressions using the REDUCE language for algebraic manipulation.