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On the global convergence of path-following methods to determine all solutions to a system of nonlinear equations

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Abstract

In this paper we prove a general theorem stating a sufficient condition for the inverse image of a point under a continuously differentiable map from ℝn to ℝk to be connected. This result is applied to the trajectories generated by the Newton flow. Several examples demonstrate the applicability of the results to nontrivial problems.

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Authors and Affiliations

  1. Institut für Numerische und Angewandte Mathematik, Georg-August Universität Göttingen, D-3400, Göttingen, Germany

    Immo Diener

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  1. Immo Diener
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This work was supported by the Deutsche Forschungsgemeinschaft.

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Diener, I. On the global convergence of path-following methods to determine all solutions to a system of nonlinear equations. Mathematical Programming 39, 181–188 (1987). https://doi.org/10.1007/BF02592951

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  • DOI: https://doi.org/10.1007/BF02592951

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