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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 428, Pages 182–195
(Mi znsl6060)
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This article is cited in 26 scientific papers (total in 26 papers)
Bounds for the inverses of generalized Nekrasov matrices
L. Yu. Kolotilina St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
The paper considers upper bounds for the infinity norm of the inverse for matrices in two subclasses of the class of (nonsingular) $H$-matrices, both of which contain the class of Nekrasov matrices. The first one has been introduced recently and consists of the so-called $S$-Nekrasov matrices. For $S$-Nekrasov matrices, the known bounds are improved. The second subclass consists of the so-called QN- (quasi-Nekrasov) matrices, which are defined in the present paper. For QN-matrices, an upper bound on the infinity norm of the inverses is established. It is shown that in application to Nekrasov matrices the new bounds are generally better than the known ones.
Key words and phrases:
$S$-Nekrasov matrix, Quasi-Nekrasov matrix, Nekrasov matrix, $H$-matrix, SDD-matrix, $S$-SDD matrix, inverse matrix, infinity norm, upper bound, Varah's bound.
Received: 15.10.2014
Citation:
L. Yu. Kolotilina, “Bounds for the inverses of generalized Nekrasov matrices”, Computational methods and algorithms. Part XXVII, Zap. Nauchn. Sem. POMI, 428, POMI, St. Petersburg, 2014, 182–195; J. Math. Sci. (N. Y.), 207:5 (2015), 786–794
Linking options:
https://www.mathnet.ru/eng/znsl6060 https://www.mathnet.ru/eng/znsl/v428/p182
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Abstract page: | 242 | Full-text PDF : | 75 | References: | 39 |
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