Abstract
The starting point of this note is a decades-old yet little-noticed sufficient condition, presented by Sassenfeld in 1951, for the convergence of the classical Gauss-Seidel method. The purpose of the present paper is to shed new light on Sassenfeld's criterion and to demonstrate that it is directly related to H-matrices. In particular, our results yield a new characterization of H-matrices. In addition, the convergence of iterative linear solvers that involve H-matrix preconditioners is briefly discussed.
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