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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 621-628, 2023/12/07
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.
Keywords: Sassenfeld criterion, convergence of iterative linear solvers, splitting methods, Gau\ss–Seidel scheme, preconditioning, H-matrices