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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 367, Pages 75–109 (Mi znsl3492)  
This article is cited in 4 scientific papers (total in 4 papers)

Bounds for the inverses of $PM$- and $PH$-matrices

L. Yu. Kolotilina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (683 kB) Citations (4)
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Abstract: 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. Bibl. – 10 titles.
Key words and phrases: $PM$-matrix, $PH$-mdtrix, inverse matrix, spectral radius, quasi-$PM$-matrix, quasi-$PH$-matrix, infinity norm.
Received: 26.03.2009
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 165, Issue 5, Pages 537–555
DOI: https://doi.org/10.1007/s10958-010-9824-1
Bibliographic databases:
UDC: 512.643
Language: Russian
Citation: L. Yu. Kolotilina, “Bounds for the inverses of $PM$- and $PH$-matrices”, Computational methods and algorithms. Part XXII, Zap. Nauchn. Sem. POMI, 367, POMI, St. Petersburg, 2009, 75–109; J. Math. Sci. (N. Y.), 165:5 (2010), 537–555
Citation in format AMSBIB
\Bibitem{Kol09}
\by L.~Yu.~Kolotilina
\paper Bounds for the inverses of $PM$- and $PH$-matrices
\inbook Computational methods and algorithms. Part~XXII
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 367
\pages 75--109
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3492}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 165
\issue 5
\pages 537--555
\crossref{https://doi.org/10.1007/s10958-010-9824-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949304280}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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