Geodesic
Bounds for the determinants and inverses of certain $H$-matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 81-102 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper studies a subclass, referred to as $PBDD(n_1,n_2)$, of the class of nonsingular $H$-matrices. A new characterization of matrices in $PBDD(n_1,n_2)$ is suggested. Two-sided bounds for the determinants of matrices in the class $PBDD(n_1,n_2)$ 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 $PBDD(n_1,n_2)$ is considered. Extensions to the case of block $k\times k$ matrices, $k\ge 2$, are addressed. 
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     title = {Bounds for the determinants and inverses of certain $H$-matrices},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a6/}
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L. Yu. Kolotilina. Bounds for the determinants and inverses of certain $H$-matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 81-102. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a6/

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