zbMATH — the first resource for mathematics

How bad are Hankel matrices? (English) Zbl 0797.65039
It is proved that the spectral condition number for any real positive definite Hankel matrix of order \(n\) is lower bounded by \(3 \cdot 2^{n- 6}\). This result appears as a consequence of viewing the corresponding scaled Vandermonde matrix as the Krylov basis matrix whose spectral condition number is bounded from below by \(3^{1\over 2} \cdot 2^{{n\over 2}-3}\). As a byproduct it is obtained a lower estimate for the spectral condition number of Vandermonde matrices with arbitrary nodes.

65F35 Numerical computation of matrix norms, conditioning, scaling
15A12 Conditioning of matrices
Full Text: DOI