Geodesic
Bounds for the inverses of generalized Nekrasov matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 182-195

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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. 
@article{ZNSL_2014_428_a12,
     author = {L. Yu. Kolotilina},
     title = {Bounds for the inverses of generalized {Nekrasov} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {182--195},
     publisher = {mathdoc},
     volume = {428},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a12/}
}
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L. Yu. Kolotilina. Bounds for the inverses of generalized Nekrasov matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 182-195. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a12/