How bad are Hankel matrices? (English) Zbl 0797.65039

Tyrtyshnikov, Evgenij E.

Numer. Math. 67, No. 2, 261-269 (1994).

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.

Reviewer: F.Luban (Bucureşti)

MSC:

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

Keywords:

conditioning; spectral condition number; real positive definite Hankel matrix; scaled Vandermonde matrix; Krylov basis matrix