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On the calculation of the exact number of zeroes of a set of equations

Zur Berechnung der genauen Zahl von Nullstellen eines Gleichungssystems

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Abstract

The number of simple zeroes common to a set of nonlinear equations is calculated exactly and analytically in terms of an integral taken over the boundary of the domain of interest. The integrand consists only of simple algebraic quantities containing the functions involved as well as their derivatives up to second order. The numerical feasibility is shown by some computed examples.

Zusammenfassung

Die genaue Anzahl der einfachen Nullstellen eines Systems nichtlinearer Gleichungen wird analytisch durch ein Integral über die Berandung des interessierenden Bereichs dargestellt. Der Integrand besteht aus einfachen algebraischen Größen, die die Funktionen samt ihren Ableitungen bis zur zweiten Ordnung enthalten. Die numerische Anwendbarkeit wird mit durchgerechneten Beispielen belegt.

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Authors and Affiliations

  1. Department of Applied Physics, State University at Groningen, Nijenborgh 18, NL-9747 AG, Groningen, The Netherlands

    B. J. Hoenders & C. H. Slump

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  1. B. J. Hoenders
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  2. C. H. Slump
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Hoenders, B.J., Slump, C.H. On the calculation of the exact number of zeroes of a set of equations. Computing 30, 137–147 (1983). https://doi.org/10.1007/BF02280784

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