Abstract
Recently the properties of Krawczyk-like iterative interval methods for the solution of systems of nonlinear equations have been discussed in several papers (e.g. [2], [3], [5], [6]). These methods converge to a solution under relatively weak conditions provided an initial inclusion vector is known. In the present paper we describe a method that improves the convergence speed for an important class of problems by using second partial derivatives. This method is particularly interesting for large systems with a Jacobi matrix whose off-diagonal coefficients are all constant.
Zusammenfassung
Kürzlich wurden in mehreren Arbeiten die Eigenschaften von Krawczyk-ähnlichen Intervalliterationsverfahren zur Lösung nichtlinearer Gleichungssysteme untersucht (z. B. [2], [3], [5], [6]). Diese Verfahren konvergieren unter verhältnismäßig schwachen Voraussetzungen gegen eine Lösung, falls eine Anfangseinschließung bekannt ist. In der vorliegenden Arbeit beschreiben wir ein Verfahren, welches die Konvergenz für eine wichtige Klasse von Anwendungen unter Verwendung zweiter partieller Ableitungen verbessert. Dieses Verfahren ist insbesondere für große Systeme interessant, deren Jacobi-Matrix außerhalb der Hauptdiagonalen konstant ist.
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Schwandt, H. Accelerating Krawczyk-like interval algorithms for the solution of nonlinear systems of equations by using second derivatives. Computing 35, 355–367 (1985). https://doi.org/10.1007/BF02240200
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DOI: https://doi.org/10.1007/BF02240200