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Einführung in die Numerische Mathematik I pp 217–285Cite as

Nullstellenbestimmung durch Iterationsverfahren. Minimierungsverfahren

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Part of the book series: Heidelberger Taschenbücher ((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

$$p(x) = {a_0} + {a_1}x + ... + {a_n}{x^n}$$

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 = ℝn so wird eine Abbildung f: ℝn → ℝn durch n reelle Funktionen f i (x l,...,x n) von n reellen Variablen x 1,...,x n beschrieben1;:

$$f(x) = \left[ {\begin{array}{*{20}{c}} {{f_1}({x^1},...,{x^n})} \\ . \\ {{f_n}({x^1},...,{x^n})} \end{array}} \right],{x^T}({x^1},...{x^n}).$$

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Würzburg, Würzburg, Deutschland

    Prof. Dr. Josef Stoer

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  1. Prof. Dr. Josef Stoer
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© 1976 Springer-Verlag Berlin Heidelberg

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Stoer, J. (1976). Nullstellenbestimmung durch Iterationsverfahren. Minimierungsverfahren. In: Einführung in die Numerische Mathematik I. Heidelberger Taschenbücher, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06864-9_5

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  • DOI: https://doi.org/10.1007/978-3-662-06864-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07831-9

  • Online ISBN: 978-3-662-06864-9

  • eBook Packages: Springer Book Archive

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