This article is cited in 6 papers

Eigenvalue estimates for Hankel matrices

N. L. Zamarashkin, E. E. Tyrtyshnikov

Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: Positive-definite Hankel matrices have an important property: the ratio of the largest and the smallest eigenvalues (the spectral condition number) has as a lower bound an increasing exponential of the order of the matrix that is independent of the particular matrix entries. The proof of this fact is related to the so-called Vandermonde factorizations of positive-definite Hankel matrices. In this paper the structure of these factorizations is studied for real sign-indefinite strongly regular Hankel matrices. Some generalizations of the estimates of the spectral condition number are suggested.

UDC: 512.64

MSC: Primary 15A18, 65F15, 15A27; Secondary 15A32, 65F35

Received: 15.06.2000

DOI: 10.4213/sm557

 English version: Sbornik: Mathematics, 2001, 192:4, 537–550

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