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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 482, Pages 184–200 (Mi znsl6836)  
This article is cited in 4 scientific papers (total in 4 papers)

New classes of nonsingular matrices and upper bounds for their inverses

L. Yu. Kolotilina

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
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Abstract: The paper introduces new classes of nonsingular matrices, which extend some known subclasses of the class of nonsingular $\mathcal{H}$-matrices, such as the Nekrasov, $Q$-Nekrasov, $\{P_1,P_2\}$-Nekrasov, and DZ matrices. For matrices in the classes introduced, upper bounds for $\|A^{-1}\|_\infty$ are derived (in a unified manner) and shown to improve the known bounds for matrices from the corresponding subclasses of nonsingular $\mathcal{H}$-matrices.
Key words and phrases: Nekrasov matrices, $Q$-Nekrasov matrices, $\{P_1,P_2\}$-Nekrasov matrices, DZ matrices, $S$-SDD matrices, $S$-Nekrasov matrices, SDD matrices, reverse matrix, infinity norm, upper bound, $\mathcal M$-matrices, $\mathcal H$-matrices.
Received: 30.09.2019
Document Type: Article
UDC: 512.643
Language: Russian
Citation: L. Yu. Kolotilina, “New classes of nonsingular matrices and upper bounds for their inverses”, Computational methods and algorithms. Part XXXII, Zap. Nauchn. Sem. POMI, 482, POMI, St. Petersburg, 2019, 184–200
Citation in format AMSBIB
\Bibitem{Kol19}
\by L.~Yu.~Kolotilina
\paper New classes of nonsingular matrices and upper bounds for their inverses
\inbook Computational methods and algorithms. Part~XXXII
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 482
\pages 184--200
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6836}
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  • https://www.mathnet.ru/eng/znsl/v482/p184
    • 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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