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Nullstellenbestimmung durch Iterationsverfahren. Minimierungsverfahren

  • Josef Stoer
Chapter
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Part of the Heidelberger Taschenbücher book series (HTB, volume 105)

Zusammenfassung

Ein wichtiges Problem ist die Bestimmung der Nullstellen ξ einer gegebenen Funktion f : f (ξ) = 0. Man denke dabei nicht nur an das Problem, die Nullstellen eines Polynoms
$$p(x) = {a_0} + {a_1}x + \cdots + {a_n}{x^n}$$
zu finden. Je nach Definition der Funktion f : E → F und der Mengen E und F kann man sehr allgemeine Probleme als eine Aufgabe der Nullstellenbestimmung auffassen. Ist z. B. E = F = ℝ n so wird eine Abbildung f : ℝ n → ℝ n durch n reelle Funktionen f i (x 1, ..., x n ) von n reellen Variablen x 1, ..., x n beschrieben1:
$$f(x) = \left[ {\begin{array}{*{20}{c}} {{{f}_{1}}({{x}^{1}}, \ldots ,{{x}^{n}})} \\ \vdots \\ {{{f}_{n}}({{x}^{1}}, \ldots ,{{x}^{n}})} \\ \end{array} } \right],{{x}^{T}} = ({{x}^{1}}, \ldots ,{{x}^{n}}).$$
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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Josef Stoer
    • 1
  1. 1.Institut für Angewandte Mathematik und StatistikUniversität WürzburgWürzburgDeutschland

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