A note on the Sassenfeld criterion and its relation to H-matrices
Numerical Analysis
2023-01-18 v2 Numerical Analysis
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.
Cite
@article{arxiv.2201.05628,
title = {A note on the Sassenfeld criterion and its relation to H-matrices},
author = {Thomas P. Wihler},
journal= {arXiv preprint arXiv:2201.05628},
year = {2023}
}