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

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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 ≥ 2 matrices satisfying joint diagonal dominance conditions is obtained. The particular cases of the bounds suggested that correspond to the infinity norm are discussed separately and compared with some known results. Bibliography: 8 titles.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    L. Yu. Kolotilina

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  1. L. Yu. Kolotilina
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Correspondence to L. Yu. Kolotilina.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 382, 2010, pp. 125–140.

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Kolotilina, L.Y. On Ostrowski’s disk theorem and lower bounds for the smallest eigenvalues and singular values. J Math Sci 176, 68–77 (2011). https://doi.org/10.1007/s10958-011-0394-7

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  • DOI: https://doi.org/10.1007/s10958-011-0394-7

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