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Sbornik: Mathematics, 2001, Volume 192, Issue 4, Pages 537–550
DOI: https://doi.org/10.1070/sm2001v192n04ABEH000557 (Mi sm557) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Eigenvalue estimates for Hankel matrices

N. L. Zamarashkin, E. E. Tyrtyshnikov

Institute of Numerical Mathematics, Russian Academy of Sciences
English version PDF (168 kB) Citations (5)
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DOI: https://doi.org/10.1070/sm2001v192n04ABEH000557
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.
Received: 15.06.2000
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 4, Pages 59–72
DOI: https://doi.org/10.4213/sm557
Bibliographic databases:
UDC: 512.64
MSC: Primary 15A18, 65F15, 15A27; Secondary 15A32, 65F35
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:85
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