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The paper considers the classes of GSDD1, GSDD 1 ∗ , and SD-SDD matrices, which contain the class of SDD (strictly diagonally dominant) matrices and are contained in the class of nonsingular H -matrices. New upper bounds on ‖ A - 1 ‖ ∞ for GSDD1, GSDD 1 ∗ , and SD-SDD matrices A, generalizing known upper bounds for S-SDD, SDD 1 ∗ , and GSDD1 matrices, are established and compared. [ABSTRACT FROM AUTHOR]

The paper suggests two general approaches to deriving upper bounds for ‖ A - 1 ‖ ∞ for some eventually H -matrices A. The approaches are illustrated by considering the classes of eventually SDD and eventually DSDD matrices, for which improvements of the known bounds are obtained. Also it is indicated that the approaches suggested are actually applicable to considerably larger matrix classes. [ABSTRACT FROM AUTHOR]