Abstract
In this paper we present and discuss a continuation method for solving certain fixed point problems in Hilbert spaces. The procedure allows to reduce progressively the residual until a desired level is reached. It is constructed combining a projected variant of Newton's method recently proposed and studied in [6] with the so-called principle of sufficiently weak increase of H. Schwetlick [9], [10]. Numerical examples illustrate the performance of the algorithm.
Zusammenfassung
Es wird eine Fortsetzungstechnik zur Lösung nichtlinearer Fixpunktprobleme in Hilberträumen vorgestellt und diskutiert. Sie benutzt projezierte Newton-Schritte zur Lösung der Teilprobleme. Numerische Beispiele illustrieren das Verhalten des Verfahrens.
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Moret, I. A continuation procedure based on projected Newton steps. Computing 43, 13–25 (1989). https://doi.org/10.1007/BF02243802
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DOI: https://doi.org/10.1007/BF02243802