Upper bounds for the infinity norm of the inverse of SDD and SS-SDD matrices

An easily calculable upper bound for the infinity norm of the inverse of SS-strictly diagonally dominant (SS-SDD) matrices, introduced by Gao and Wang in 1992, is obtained in this paper. Applying that bound to SDD matrices, we improve the Varah bound. We also introduce an iterative procedure for obtaining sharper bounds, accompanied with some open questions.