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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 504, Pages 70–101
(Mi znsl7112)
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Further block generalizations of Nekrasov matrices
L. Yu. Kolotilina St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
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
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
Linking options:
https://www.mathnet.ru/eng/znsl7112 https://www.mathnet.ru/eng/znsl/v504/p70
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