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Eigenwertprobleme

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Book cover Numerische Mathematik 2

Part of the book series: Springer-Lehrbuch ((SLB))

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Zusammenfassung

Viele praktische Probleme in den Ingenieur- und Naturwissenschaften führen auf Eigenwertprobleme. Zu diesen Problemen gehört typischerweise ein überbestimmtes Gleichungssystem, etwa von n + 1 Gleichungen für n Unbekannte, ξ 1, ..., ξ n , der Form

$$F(x;\lambda ) \equiv \left[ {\begin{array}{*{20}{c}} {{{f}_{1}}({{\xi }_{1}},...,{{\xi }_{n}};\lambda )} \\ {{{f}_{{n + 1}}}({{\xi }_{1}},...,{{\xi }_{n}};\lambda )} \\ \end{array} } \right] = 0,$$
(6.0.1)

in denen die Funktionen f i von einem weiteren Parameter λ abhängen. Gewöhnlich besitzt (6.0.1) nur für spezielle Werte λ = λ i , i = 1, 2, ..., dieses Parameters Lösungen x = [ξ 1, ..., ξ n ], die natürlich von λi abhängen, x = x(λ i ). Diese Werte λ i heißen Eigenwerte des Eigenwertproblems (6.0.1), und eine zugehörige Lösung x(λ i ) Eigenlösung zum Eigenwert λ i .

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Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, 97074, Würzburg, Deutschland

    Prof. Dr. Josef Stoer

  2. Zentrum Mathematik, Technische Universität München, Arcisstr. 21, 80333, München, Deutschland

    Prof. Dr. Roland Bulirsch

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  1. Prof. Dr. Josef Stoer
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  2. Prof. Dr. Roland Bulirsch
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Stoer, J., Bulirsch, R. (2000). Eigenwertprobleme. In: Numerische Mathematik 2. Springer-Lehrbuch. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09025-1_1

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  • DOI: https://doi.org/10.1007/978-3-662-09025-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67644-7

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