Abstract
The paper studies a subclass, referred to as PBDD(n1, n2), of the class of nonsingular H-matrices. A new characterization of matrices in PBDD(n1, n2) is suggested. Two-sided bounds for the determinants of matrices in the class PBDD(n1, n2) are derived, and their applications to strictly diagonally dominant matrices and to matrices with the Ostrowski-Brauer diagonal dominance are presented. An upper bound for the infinity norms of the inverses of matrices in PBDD(n1, n2) is considered. Extensions to the case of block k × k matrices, k ≥ 2, are addressed. Bibliography: 17 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 81–102.
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Kolotilina, L.Y. Bounds for the determinants and inverses of certain H-matrices. J Math Sci 150, 1961–1972 (2008). https://doi.org/10.1007/s10958-008-0111-3
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DOI: https://doi.org/10.1007/s10958-008-0111-3