Asymptotically Optimal Lower Bounds for the Condition Number of a Real Vandermonde Matrix
Ren‐Cang Li · SIAM Journal on Matrix Analysis and Applications · 2006
Lower bounds on the condition number $\min\kappa_p(V)$ of a real Vandermonde matrix V are established in terms of the dimension n or n and the largest absolute value among all nodes that define the Vandermonde matrix. All bounds here are asymptotically sharp, similar to those in Beckermann (Numer. Math., 85 (2000), pp. 553–577), but bounds here are sharper and cover more cases. Also, qualitative behaviors of $\min\kappa_p(V)$, as well as nearly optimally conditioned real Vandermonde matrices, as functions of the largest absolute value among all nodes are obtained.