Geodesic
On perfect conditioning of Vandermonde matrices on the unit circle
The electronic journal of linear algebra, Tome 16 (2007), pp. 157-161.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $K, M \in \Bbb N$ with $K M$, and define a square $K\times K$ Vandermonde matrix $A = A (\tau,\vec n)$ with nodes on the unit circle: $A_{p,q} = \exp (- j2\pi pn_q\tau/K)$; $p,q = 0,1,\dots,K-1$, where $n_q\in \{0,1,\dots,M-1\}$ and $n_0 $. Such matrices arise in some types of interpolation problems. In this paper, necessary and sufficient conditions are presented on the vector $\vec n$ so that a value of $\tau\in \Bbb R$ 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.
Classification : 15A12, 65F35
Keywords: vandermonde matrix, condition number, perfect conditioning 
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     title = {On perfect conditioning of {Vandermonde} matrices on the unit circle},
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Berman, Lihu; Feuer, Arie. On perfect conditioning of Vandermonde matrices on the unit circle. The electronic journal of linear algebra, Tome 16 (2007), pp. 157-161. http://geodesic.mathdoc.fr/item/ELA_2007__16__a25/