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Zap. Nauchn. Sem. POMI, 2007, Volume 346, Pages 81–102 (Mi znsl89)  

This article is cited in 11 scientific papers (total in 11 papers)

Bounds for the determinants and inverses of certain $H$-matrices

L. Yu. Kolotilina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The paper studies a subclass, referred to as $PBDD(n_1,n_2)$, of the class of nonsingular $H$-matrices. A new characterization of matrices in $PBDD(n_1,n_2)$ is suggested. Two-sided bounds for the determinants of matrices in the class $PBDD(n_1,n_2)$ are derived, and their applications to strictly diagonally dominant matrices and to matrices with the Ostrowski–Brauer diagonal dominance are presented. An upper bound for the infinity norms of the inverses of matrices in $PBDD(n_1,n_2)$ is considered. Extensions to the case of block $k\times k$ matrices, $k\ge 2$, are addressed.

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English version:
Journal of Mathematical Sciences (New York), 2008, 150:2, 1961–1972

Bibliographic databases:

UDC: 512.643
Received: 04.10.2007

Citation: L. Yu. Kolotilina, “Bounds for the determinants and inverses of certain $H$-matrices”, Computational methods and algorithms. Part XX, Zap. Nauchn. Sem. POMI, 346, POMI, St. Petersburg, 2007, 81–102; J. Math. Sci. (N. Y.), 150:2 (2008), 1961–1972

Citation in format AMSBIB
\Bibitem{Kol07}
\by L.~Yu.~Kolotilina
\paper Bounds for the determinants and inverses of certain $H$-matrices
\inbook Computational methods and algorithms. Part~XX
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 346
\pages 81--102
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl89}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2469442}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 150
\issue 2
\pages 1961--1972
\crossref{https://doi.org/10.1007/s10958-008-0111-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41149166739}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. Yu. Kolotilina, “Improving Chistyakov's bounds for the Perron root of a nonnegative matrix”, J. Math. Sci. (N. Y.), 150:2 (2008), 1973–1981  mathnet  crossref  mathscinet
    2. Kolotilina L.Yu., “Bounds for the infinity norm of the inverse for certain $M$- and $H$-matrices”, Linear Algebra Appl., 430:2-3 (2009), 692–702  crossref  mathscinet  zmath  isi  elib  scopus
    3. Li Hou-Biao, Huang Ting-Zhu, Li Hong, “Some New Results on Determinantal Inequalities and Applications”, J. Inequal. Appl., 2010, 847357, 16 pp.  mathscinet  zmath  isi
    4. Cvetkovic L., Kostic V., Doroslovacki K., “Max-Norm Bounds for the Inverse of S-Nekrasov Matrices”, Appl. Math. Comput., 218:18 (2012), 9498–9503  crossref  mathscinet  zmath  isi  scopus
    5. L. Yu. Kolotilina, “Some characterizations of Nekrasov and $S$-Nekrasov matrices”, J. Math. Sci. (N. Y.), 207:5 (2015), 767–775  mathnet  crossref
    6. L. Yu. Kolotilina, “Bounds for the determinants of Nekrasov and $S$-Nekrasov matrices”, J. Math. Sci. (N. Y.), 207:5 (2015), 776–785  mathnet  crossref
    7. L. Yu. Kolotilina, “Bounds for the inverses of generalized Nekrasov matrices”, J. Math. Sci. (N. Y.), 207:5 (2015), 786–794  mathnet  crossref
    8. L. Yu. Kolotilina, “Bounds on the $l_\infty$ norm of inverses for certain block matrices”, J. Math. Sci. (N. Y.), 216:6 (2016), 816–824  mathnet  crossref  mathscinet
    9. L. Yu. Kolotilina, “New subclasses of the class of $\mathcal H$-matrices and related bounds for the inverses”, J. Math. Sci. (N. Y.), 224:6 (2017), 911–925  mathnet  crossref  mathscinet
    10. L. Yu. Kolotilina, “On block generalizations of $\mathcal H$-matrices”, J. Math. Sci. (N. Y.), 224:6 (2017), 926–936  mathnet  crossref  mathscinet
    11. L. Yu. Kolotilina, “O matritsakh Dashnitsa–Zusmanovicha (DZ) i matritsakh tipa Dashnitsa–Zusmanovicha (DZT) i ikh obratnykh”, Chislennye metody i voprosy organizatsii vychislenii. XXXI, Zap. nauchn. sem. POMI, 472, POMI, SPb., 2018, 145–165  mathnet
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