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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 504, Pages 70–101 (Mi znsl7112)  

Further block generalizations of Nekrasov matrices

L. Yu. Kolotilina

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
References:
Abstract: The paper continues the study of block generalizations of Nekrasov matrices and introduces two new classes of the so-called $\widetilde{\mathrm{G}}\mathrm{N}$ and $\mathrm{BJN}$ matrices and compares them with the previously introduced class of $\mathrm{GN}$ matrices. Different properties of $\widetilde{\mathrm{G}}\mathrm{N}$ and $\mathrm{BJN}$ matrices are established. In particular, it is proved that the classes $\{\widetilde{\mathrm{G}}\mathrm{N}\}$ and $\{\mathrm{BJN}\}$ are closed with respect to Schur complements and monotone with respect to block partitioning. Also upper bounds for the norms of inverses $\|A^{-1}\|_\infty$ of $\mathrm{GN}$, $\widetilde{\mathrm{G}}\mathrm{N}$, and $\mathrm{BJN}$ matrices $A$ are considered. General results obtained are specialized to the case of block two-by-two matrices with scalar first diagonal block.
Key words and phrases: Nekrasov matrices, $\mathrm{GN}$ matrices, $\widetilde{\mathrm{G}}\mathrm{N}$, $\mathrm{BJN}$ matrices, nonsingular $\mathcal{H}$-matrices, $\mathcal{M}$-matrices, $\mathrm{SDD}$ matrices, upper bounds for the inverse.
Received: 20.10.2021
Document Type: Article
UDC: 512.643
Language: Russian
Citation: L. Yu. Kolotilina, “Further block generalizations of Nekrasov matrices”, Computational methods and algorithms. Part XXXIV, Zap. Nauchn. Sem. POMI, 504, POMI, St. Petersburg, 2021, 70–101
Citation in format AMSBIB
\Bibitem{Kol21}
\by L.~Yu.~Kolotilina
\paper Further block generalizations of Nekrasov matrices
\inbook Computational methods and algorithms. Part~XXXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2021
\vol 504
\pages 70--101
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7112}
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