# The condition number of real Vandermonde, Krylov and positive definite Hankel matrices

@article{Beckermann2000TheCN, title={The condition number of real Vandermonde, Krylov and positive definite Hankel matrices}, author={Bernhard Beckermann}, journal={Numerische Mathematik}, year={2000}, volume={85}, pages={553-577} }

Summary. We show that the Euclidean condition number of any positive definite Hankel matrix of order
$n\geq 3$ may be bounded from below by
$\gamma^{n-1}/(16n)$ with
$\gamma=\exp(4 \cdot{\it Catalan}/\pi) \approx 3.210$, and that this bound may be improved at most by a factor
$8 \gamma n$. Similar estimates are given for the class of real Vandermonde matrices, the class of row-scaled real Vandermonde matrices, and the class of Krylov matrices with Hermitian argument. Improved bounds are…

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