Abstract
Several orthogonal-invariant fixpoint theorems for the convergence of the Gauss-Newton Method are given which reduce to well-known Newton-Attraction theorems in case of a system of nonlinear equations. Subsequently this result is extended to the Levenberg-Morrison-Marquardt Algorithm.
Zusammenfassung
Für die Konvergenz des Gauß-Newton-Verfahrens werden mehrere Fixpunktsätze angegeben, die sich auf bekannte Fixpunktsätze für das Newtonverfahren im Falle von nichtlinearen Gleichungssystemen reduzieren. Dieses Ergebnis wird anschließend auf das Levenberg-Morrison-Marquardt-Verfahren erweitert.
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Häußler, W.M. A local convergence analysis for the Gauss-Newton and Levenberg-Morrison-Marquardt Algorithms. Computing 31, 231–244 (1983). https://doi.org/10.1007/BF02263433
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DOI: https://doi.org/10.1007/BF02263433