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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 382, Pages 125–140 (Mi znsl3865)  
This article is cited in 2 scientific papers (total in 2 papers)

On Ostrowski's disk theorem and lower bounds for the smallest eigenvalues and singular values

L. Yu. Kolotilina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (209 kB) Citations (2)
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Abstract: The paper refines the classical Ostrowski disk theorem and suggests lower bounds for the smallest-in-modulus eigenvalue and the smallest singular value of a square matrix under certain diagonal dominance conditions. A lower bound for the smallest-in-modulus eigenvalue of a product of $m\ge2$ matrices satisfying joint diagonal dominance conditions is obtained. The particular cases of the bounds suggested that correspond to the infinity norm are discussed and compared with some known results. Bibl. 9 titles.
Key words and phrases: disk theorem, lower bound, smallest-in-modulus eigenvalue, smallest singular value, diagonal dominance conditions, nonsingular $M$-matrix, $H$-matrix.
Received: 03.11.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 176, Issue 1, Pages 68–77
DOI: https://doi.org/10.1007/s10958-011-0394-7
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: L. Yu. Kolotilina, “On Ostrowski's disk theorem and lower bounds for the smallest eigenvalues and singular values”, Computational methods and algorithms. Part XXIII, Zap. Nauchn. Sem. POMI, 382, POMI, St. Petersburg, 2010, 125–140; J. Math. Sci. (N. Y.), 176:1 (2011), 68–77
Citation in format AMSBIB
\Bibitem{Kol10}
\by L.~Yu.~Kolotilina
\paper On Ostrowski's disk theorem and lower bounds for the smallest eigenvalues and singular values
\inbook Computational methods and algorithms. Part~XXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 382
\pages 125--140
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3865}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 176
\issue 1
\pages 68--77
\crossref{https://doi.org/10.1007/s10958-011-0394-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958269670}
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  • https://www.mathnet.ru/eng/znsl/v382/p125
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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