Abstract
New sufficient conditions for the monotone convergence of Newton's method for solving nonlinear systems of equations are given. These conditions are affine-invariant and less restrictive than the hypothesis of Baluev's theorem.
Zusammenfassung
Neue hinreichende Bedingungen für die monotone Konvergenz der Newton-Methode für die Lösung nichtlinearer Gleichung werden gegeben. Diese Bedingungen sind affin-invariant und allgemeiner als die Voraussetzungen des Satzes von Baluev.
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The paper was written while the first author held an Andrew W. Mellon Postdoctoral Fellowship at the University of Pittsburgh. The work of the second author was in part supported by the National Science Foundation under grant MCS-78-05299.
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Potra, F.A., Rheinboldt, W.C. On the monotone convergence of Newton's method. Computing 36, 81–90 (1986). https://doi.org/10.1007/BF02238194
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DOI: https://doi.org/10.1007/BF02238194