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. Bibliography: 15 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 428, 2014, pp. 152–165.
Translated by L. Yu. Kolotilina.
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Kolotilina, L.Y. Some Characterizations of Nekrasov and S-Nekrasov Matrices. J Math Sci 207, 767–775 (2015). https://doi.org/10.1007/s10958-015-2399-0
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DOI: https://doi.org/10.1007/s10958-015-2399-0