Abstract
A Gauss-Newton-like method for solving singular nonlinear equations is presented. The local convergence analysis shows that this method converges quadratically. The algorithm requires second derivative information in the formF″ ab only, which makes it attractive from the viewpoint of computational effort.
Zusammenfassung
Ein Gauß-Newton-ähnliches Verfahren zur Lösung singulärer nichtlinearer Gleichungssysteme wird vorgestellt. Die Konvergenzanalyse zeigt, daß das Verfahren lokal quadratisch konvergiert. Der Algorithmus ist effektiv, implementierbar, da die von ihm benötigten Informationen 2. Ordnung nur in der GestaltF″ ab vorkommen.
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Hoy, A. An efficiently implementable Gauss-Newton-like method for solving singular nonlinear equations. Computing 41, 107–122 (1989). https://doi.org/10.1007/BF02238733
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DOI: https://doi.org/10.1007/BF02238733