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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.

##### MSC:
 65F35 Numerical computation of matrix norms, conditioning, scaling 15A12 Conditioning of matrices
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