Lower bounds for the condition number of Vandermonde matrices

SummaryWe derive lower bounds for the ∞-condition number of then×n-Vandermonde matrixVn(x) in the cases where the node vectorxT=[x1, x2,...,xn] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow exponentially inn. withO(2n) andO(2n/2), respectively. We also compute the optimal spectral condition numbers ofVn(x) for the two node configurations (including the optimal nodes) and compare them with the bounds obtained.