, Volume 26, Issue 4, pp 315–326 | Cite as

On the accurate determination of nonisolated solutions of nonlinear equations

  • H. Weber
  • W. Werner


A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.


Computational Mathematic Nonlinear Equation Efficient Method Accurate Determination Accurate Solution 
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Über die exakte Bestimmung nicht-isolierter Lösungen nichtlinearer Gleichungssysteme


Es wird eine einfache, aber wirkungsvolle Methode zur exakten Lösung eines nichtlinearen Gleichungssystems, dessen Funktionalmatrix in der Lösung singulär ist, vorgestellt. Dies wird durch eine Vergrößerung des Gleichungssystems zu einem höherdimensionalen Gleichungssystem, dessen entsprechende Lösung isoliert ist, erreicht. Diese Lösung kann daher z. B. mit dem Newton-Verfahren, das lokal mindestens quadratisch konvergent und selbstkorrigierend ist, mit großer Genauigkeit bestimmt werden.


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • H. Weber
    • 1
  • W. Werner
    • 2
  1. 1.Lehrstuhl Mathematik IIIUniversität DortmundDortmund 50Federal Republic of Germany
  2. 2.Fachbereich MathematikJohannes-Gutenberg-UniversitätMainzFederal Republic of Germany

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