Summary
In this paper we prove the convergence of the symmetric successive overrelaxation method if it is applied to certain nonlinear systems of simultaneous equations. These equations are obtained, for example, by discretizing nonlinear elliptic partial differential equations.
Zusammenfassung
In der vorliegenden Arbeit wird für die Konvergenz des symmetrischen Relaxationsverfahrens (SSOR-Verfahren) bei Anwendung auf eine Klassenichtlinearer Gleichungssysteme die globale Konvergenz bewiesen. Diese Gleichungssysteme treten z.B. bei der Diskretisierung nichtlinearer partieller Differentialgleichungen auf.
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Herrn Helmut Brakhage, Kaiserslautern, anläßlich seines sechzigsten Geburtstages am 8. 7. 1986 gewidmet
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Alefeld, G., Volkmann, P. Zur Konvergenz des SSOR-Verfahrens für nichtlineare Gleichungssysteme. Numer. Math. 50, 111–121 (1986). https://doi.org/10.1007/BF01389671
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DOI: https://doi.org/10.1007/BF01389671