LAUSR

The paper introduces new subclasses, called Pℋ$$ \mathrm{\mathscr{H}} $$N(π) and Pℋ$$ \mathrm{\mathscr{H}} $$QN(π), of (nonsingular) ℋ$$ \mathrm{\mathscr{H}} $$-matrices of order n dependent on a partition π of the index set {1, . . ., n}, which generalize the classes Pℋ$$ \mathrm{\mathscr{H}} $$(π), introduced previously, and contain, in particular, such subclasses as those of strictly diagonally dominant (SDD), Nekrasov, S-SDD, S-Nekrasov, QN, and Pℋ$$ \mathrm{\mathscr{H}} $$(π) matrices. Properties of the matrices introduced are studied, and upper bounds on their inverses in l∞ norm are obtained. Block generalizations of the classes Pℋ$$ \mathrm{\mathscr{H}} $$N(π) and Pℋ$$ \mathrm{\mathscr{H}} $$QN(π) in the sense of Robert are considered.Also a general approach to defining subclasses Kπ$$ {\mathcal{K}}^{\pi } $$ of the class ℋ$$ \mathrm{\mathscr{H}} $$ containing a given subclass K$$ \mathcal{K} $$ ⊂ ℋ$$ \mathrm{\mathscr{H}} $$ and dependent on a partition π is presented.