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Weber's problem and weiszfeld's algorithm in general spaces

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⋯Wenn aber schon einmal Theorie getrieben werden soll, (man möchte die Vorliebe dafür angesichts gewisser missglückter Erscheinungen ja allerdings manchmal zum Teufel wünschen) so ist als eine ihrer Formen auch diejenige nötig, die die Abstraktion auf die Spitze treibt.

Alfred Weber, 1909

Abstract

For solving the Euclidean distance Weber problem Weiszfeld proposed an iterative method. This method can also be applied to generalized Weber problems in Banach spaces. Examples for generalized Weber problems are: minimal surfaces with obstacles, Fermat's principle in geometrical optics and brachistochrones with obstacles.

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  1. Institut für Angewandte Mathematik, Universität Hamburg, Hamburg, Germany

    Ulrich Eckhardt

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  1. Ulrich Eckhardt
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Eckhardt, U. Weber's problem and weiszfeld's algorithm in general spaces. Mathematical Programming 18, 186–196 (1980). https://doi.org/10.1007/BF01588313

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