Bounds for the determinants and inverses of certain H-matrices

The paper studies a subclass, referred to as PBDD(n1, n 2), 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(n 1, n2) is considered. Extensions to the case of block k × k matrices, k ≥ 2, are addressed. Bibliography: 17 titles. © 2008 Springer Science+Business Media, Inc.