Lower bounds for the condition number of the Vandermonde matrix

We derive lower bounds for the oo-condition number of the n x n- Vandermonde matrix V,(x) in the cases where the node vector xr= [x~, x2 ..... x,] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow exponentially in n, with 0(2") and O(2"/2), respectively. We also compute the optimal spectral condition numbers of V.(x) for the two node configurations (including the optimal nodes) and compare them with the bounds obtained.