Abstract
We present an iterative algorithm for solving nonlinear systems of equations which is monotonically and superlinearly convergent for a large class of problems. In the construction of the algorithm we use some fixed bounds of the second derivatives. For convex mappings the algorithm reduces to the Newton-Fourier method.
Zusammenfassung
Wir stellen ein Iterationsverfahren zur Auflösung nichtlinearer Gleichungssysteme vor welches für eine große Klasse von Problemen monoton und überlinear konvergiert. Zur Konstruktion des Verfahrens werden feste Schranken für die zweite Ableitung verwendet. Für konvexe Abbildungen geht das Verfahren in das Newton-Fourier-Verfahren über.
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This work was supported in part by the National Science Foundation under Grant DMS-8503365.
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Potra, F.A. On a monotone Newton-like method. Computing 39, 233–246 (1987). https://doi.org/10.1007/BF02309557
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DOI: https://doi.org/10.1007/BF02309557