On the inversion of the Vandermonde matrix

The inversion of the Vandermonde matrix has received much attention for its role in the solution of some problems of numerical analysis and control theory. This work deals with the problem of getting an explicit formula for the generic element of the inverse. We derive two algorithms in O(n2) and O(n3) and compare them with the Parker–Traub and the Björck–Pereyra algorithms.