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Mat. Sb., 2001, Volume 192, Number 4, Pages 59–72 (Mi msb557)  

This article is cited in 2 scientific papers (total in 2 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.

DOI: https://doi.org/10.4213/sm557

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

Bibliographic databases:

UDC: 512.64
MSC: Primary 15A18, 65F15, 15A27; Secondary 15A32, 65F35
Received: 15.06.2000

Citation: N. L. Zamarashkin, E. E. Tyrtyshnikov, “Eigenvalue estimates for Hankel matrices”, Mat. Sb., 192:4 (2001), 59–72; Sb. Math., 192:4 (2001), 537–550

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Olshevsky A., “Eigenvalue clustering, control energy, and logarithmic capacity”, Syst. Control Lett., 96 (2016), 45–50  crossref  mathscinet  zmath  isi  scopus
    2. Dette H., Tomecki D., “Hankel Determinants of Random Moment Sequences”, J. Theor. Probab., 30:4 (2017), 1539–1564  crossref  mathscinet  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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