On the inversion of the Vandermonde matrix A. Eisinberg, G. Fedele * Dip. Elettronica Informatica e Sistemistica, Universita ` degli Studi della Calabria, 87036 Rende (Cs), Italy Abstract 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(n 2 ) and O(n 3 ) and compare them with the Parker–Traub and the Bjo ¨ rck–Pereyra algorithms. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Vandermonde matrices; Parker–Traub algorithm; Bjo ¨ rck–Pereyra algorithm 1. Introduction We consider the inversion of the Vandermonde matrix, V ðx 1 ; x 2 ; ... ; x n Þ¼ 1 x 1 ... x n1 1 1 x 2 ... x n1 2 . . . . . . . . . 1 x n ... x n1 n 0 B B B B @ 1 C C C C A ; 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.06.014 * Corresponding author. E-mail address: fedele@si.deis.unical.it (G. Fedele). Applied Mathematics and Computation 174 (2006) 1384–1397 www.elsevier.com/locate/amc