Geodesic
Some characterizations of Nekrasov and $S$-Nekrasov matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 152-165

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It is known that the Nekrasov and $S$-Nekrasov matrices form subclasses of (nonsingular) $H$-matrices. The paper presents some necessary and sufficient conditions for a square matrix with complex entries to be a Nekrasov and an $S$-Nekrasov matrix. In particular, characterizations of the Nekrasov and $S$-Nekrasov matrices in terms of the diagonal column scaling matrices transforming them into strictly diagonally dominant matrices are obtained. 
@article{ZNSL_2014_428_a10,
     author = {L. Yu. Kolotilina},
     title = {Some characterizations of {Nekrasov} and $S${-Nekrasov} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {152--165},
     publisher = {mathdoc},
     volume = {428},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a10/}
}
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L. Yu. Kolotilina. Some characterizations of Nekrasov and $S$-Nekrasov matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 152-165. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a10/