Upper bounds for $\|A^{-1}\|_\infty$ for some eventually $\mathcal{H}$-matrices

The paper suggests two general approaches to deriving upper bounds for $\|A^{-1}\|_\infty$ for some eventually $\mathcal{H}$-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 derived. Also it is indicated that the approaches suggested are actually applicable to considerably larger matrix classes.