Volume 58, pp. 621-628, 2023.

A generalized Sassenfeld criterion and its relation to H-matrices

Thomas P. Wihler


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 Gau\ss–Seidel method. The purpose of the present paper is to shed new light on Sassenfeld's criterion and to demonstrate that it is closely related to H-matrices. In particular, our main result yields a novel characterization of H-matrices. In addition, a new convergence estimate for iterative linear solvers, which involve H-matrix preconditioners, is briefly discussed.

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Key words

Sassenfeld criterion, convergence of iterative linear solvers, splitting methods, Gau\ss–Seidel scheme, preconditioning, H-matrices

AMS subject classifications

15B48, 65F08, 65F10

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