Abstract:
The paper is mainly devoted to studying the so-called Dashnic–Zusmanovich type (DZT) matrices, introduced recently. Interrelations among the DZT matrices and related subclasses of the class of nonsingular $\mathcal{H}$-matrices, namely, the Dashnic–Zusmanovich (DZ) and $S$-SDD matrices are considered. Upper bounds for the $l_\infty$-norm of the inverses to DZT, DZ, and strictly diagonally dominant (SDD) matrices are obtained.
Key words and phrases:nonsingular $\mathcal H$-matrices, Dashnic–Zusmanovich (DZ) matrices, Dashnic–Zusmanovich type (DZT) matrices, $S$-SDD matrices, SDD matrices, upper bounds, $l_\infty$-norm, inverse matrices, transvections.
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