ELA, Volume 16, pp. 157-161, July 2007, abstract.

On Perfect Conditioning of Vandermonde Matrices 
on the Unit Circle

Lihu Berman and Arie Feuer

Let K,M be natural numbers with K<M, and define a square KxK
Vandermonde matrix A=A(tau,n) with nodes on the unit circle: 

  A_{p,q} = exp (-j 2pi p n_q tau/K);

p,q=0,1,...,K-1, where n_q belongs to {0,1,...,M-1} and
n_0<n_1<....<n_{K-1}. Such matrices arise in some types of
interpolation problems. In this paper, necessary and sufficient 
conditions are presented on the vector n so that a real value of 
tau can be found to achieve perfect conditioning of A. A simple 
test to check the condition is derived and the corresponding value 
of tau is found.