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

  title={The condition number of real Vandermonde, Krylov and positive definite Hankel matrices},
  author={Bernhard Beckermann},
  journal={Numerische Mathematik},
  • B. Beckermann
  • Published 1 June 2000
  • Mathematics, Computer Science
  • Numerische Mathematik
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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