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A Classification of Quasi-Newton Methods

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Abstract

In this paper, we consider quasi-Newton methods of the form x k+1=x k +Λ k f(x k ), k=0,1,. . . , for the solution of the system of nonlinear equations f(x)=0. We present a classification of such methods based on different structures for the matrix Λ k and various criteria for its computation, issued from three different formulae. Many known methods can be put into this framework and new methods are also obtained.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, FRE CNRS 2222, UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655-, Villeneuve d'Ascq Cedex, France

    C. Brezinski

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Brezinski, C. A Classification of Quasi-Newton Methods. Numerical Algorithms 33, 123–135 (2003). https://doi.org/10.1023/A:1025551602679

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