Abstract:
The paper considers some subclasses of the class of nonsingular $\mathcal{H}$-matrices whose definitions involve matrix sparsity pattern. For matrices $A$ in these subclasses, upper bounds for $\|A^{-1}\|_\infty$ are derived and shown to be sharper than the corresponding bounds ignoring matrix sparsity.
Key words and phrases:inverse matrices, $l_\infty$-norm, sparsity pattern, nonsingular $\mathcal H$-matrices, $S$-SOB matrices, $S$-OB matrices, $S$-SDDS matrices, $S$-SDD matrices, OBS matrices, OB (DSDD) matrices, SDD matrices, upper bounds.
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