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A reliable method for solving nonlinear systems of equations of few variables

Eine zuverlässige Methode zur Lösung nichtlinearer Gleichungssysteme mit wenigen Unbekannten


The paper gives a new method for finding solutions of a nonlinear system of equations in a compactm-dimensional interval (rectangle). This method can be considered as a generalization of the so-called exclusion methods and also as a simplification of a method (given by the author) for finding the global minimum in a compactm-dimensional interval.


Die Arbeit stellt eine neue Methode zur Bestimmung der Lösungen eines nichtlinearen Gleichungssystems in einem kompaktenm-dimensionalen Intervall (Rechteck) dar. Die Methode kann als Verallgemeinerung der sogenannten Ausschließungsmethoden betrachtet werden und auch als Vereinfachung einer (vom Autor angegebenen) Methode zur Bestimmung des globalen Minimums angesehen werden.

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Kálovics, F. A reliable method for solving nonlinear systems of equations of few variables. Computing 48, 291–302 (1992). https://doi.org/10.1007/BF02238639

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AMS Subject Classification

  • 65H10

Key words

  • Indicator function
  • cover system
  • minimum vector
  • bound of derivatives