Some characterizations of Nekrasov and \(S\)-Nekrasov matrices. (English. Russian original) Zbl 1332.15046
J. Math. Sci., New York 207, No. 5, 767-775 (2015); translation from Zap. Nauchn. Semin. POMI 428, 152-165 (2014).
Summary: 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.
MSC:
| 15A45 | Miscellaneous inequalities involving matrices |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
inequalities involving matrices; Nekrasov matrices; \(H\)-matrices; scaling matrices; strictly diagonally dominant matricesReferences:
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