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Über die Konvergenzordnung Gewisser Rang-2-Verfahren zur Minimierung von Funktionen

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Book cover Numerische Methoden bei Optimierungsaufgaben

Abstract

In this paper the local convergence behaviour of one of Broyden’s rank-two-algorithms for the minimization of functions on Rn is investigated.

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Literatur

  1. Broyden, C.G. (1967): Quasi-Newton methods and their application to function minimization. Math. Comp. 21, 368–381.

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  2. Broyden, C.G. (1970): The convergence of a class of double-rank minimization algorithms. Part I: J. Math. Applics 6, 76, Part II: ibid. 6, 222.

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  3. Dixon, L.C.W. (1972): Quasi-Newton algorithms generate identical points. Math. Progr. 2, 383–387.

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  4. Powell, M.J.D. (1971): On the convergence of the variable metric algorithm. J. Inst. Math. Applies 7, 21–36.

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  5. Powell, M.J.D. (1972): Some properties of the variable metric algorithm. In Lootsma, F.A. (ed.): Numerical Methods for non-linear optimization. London, Academic Press 1972.

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  6. Ortega, J.M. und W.C. Rheinboldt (1970): Iterative solution of nonlinear equations in several variables. New York and London, Academic Press 1970.

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  7. Schuller, G. (1972): Dissertation Universität Würzburg.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Würzburg, 8700, Würzburg, Kaiserstraße 27, Deutschland

    Dr. Günther Schuller & Prof. Dr. Josef Stoer

Authors
  1. Dr. Günther Schuller
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  2. Prof. Dr. Josef Stoer
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Editor information

Editors and Affiliations

  1. Hamburg, Germany

    L. Collatz

  2. Enschede, Netherlands

    W. Wetterling

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© 1974 Springer Basel AG

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Schuller, G., Stoer, J. (1974). Über die Konvergenzordnung Gewisser Rang-2-Verfahren zur Minimierung von Funktionen. In: Collatz, L., Wetterling, W. (eds) Numerische Methoden bei Optimierungsaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 23. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5321-7_10

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  • DOI: https://doi.org/10.1007/978-3-0348-5321-7_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5322-4

  • Online ISBN: 978-3-0348-5321-7

  • eBook Packages: Springer Book Archive

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