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Bounds for the inverses of PM- and PH-matrices

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The paper presents new bounds for the inverses of the so-called PM- and PH-matrices. Also bounds for the spectral radii of the inverses to PM- and PH-matrices are obtained, and the monotonicity of these bounds with respect to the underlying partition of the index set is established. Finally, the so-called quasi-PM- and quasi-PH-matrices are introduced, and bounds for the inverses of such matrices are suggested. Bibliography: 10 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. 367, 2009, pp. 75–109.

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Kolotilina, L.Y. Bounds for the inverses of PM- and PH-matrices. J Math Sci 165, 537–555 (2010). https://doi.org/10.1007/s10958-010-9824-1

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  • DOI: https://doi.org/10.1007/s10958-010-9824-1

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