Ela on Perfect Conditioning of Vandermonde Matrices on the Unit Circle ∗

@inproceedings{Berman2007ElaOP,
  title={Ela on Perfect Conditioning of Vandermonde Matrices on the Unit Circle ∗},
  author={L. Berman and A. Feuer},
  year={2007}
}
Let K, M ∈ N with K < M , and define a square K × K Vandermonde matrix A = A τ,−→n with nodes on the unit circle: Ap,q = exp (−j2πpnqτ/K) ; p, q = 0, 1, ...,K − 1, where nq ∈ {0, 1, ...,M − 1} and n0 < n1 < .... < nK−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 value of τ ∈ R can be found to achieve perfect conditioning of A. A simple test to check the condition is derived and the… CONTINUE READING