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On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators

Über die Konvergenz gewisser Quasi-Newton-Verfahren für nichtlineare Gleichungen mit nichtdifferenzierbaren Operatoren

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Abstract

In this paper, we study the convergence of some quasi-Newton methods for solving nonlinear equationAx+g(x)=0 in a domainD⊄R n, whereA is ann×n matrix andg is a nondifferentiable but Lipschitz continuous operator. By interval analysis, we give a new convergence theorem of the methods.

Zusammenfassung

In der vorliegenden Arbeit wird die Konvergenz gewisser Quasi-Newton-Verfahren zur Lösung von nichtlinearen GleichungenAx+g(x)=0 aufD⊄R n untersucht, wobeiA eine (n×n)-Matrix undg ein nichtdifferenzierbarer, aber Lip-schitz-stetiger Operator ist. Mittels intervallanalytischer Techniken wird ein neuer Konvergenzsatz für die Verfahren hergeleitet.

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Authors and Affiliations

  1. School of Mathematics, The University of New South Wales, P.O. Box 1, 2033, Kensington, NSW, Australia

    X. Chen

  2. Department of Mathematics Faculty of Science, Ehime University, 790, Matsuyama, Japan

    T. Yamamoto

Authors
  1. X. Chen
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  2. T. Yamamoto
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Chen, X., Yamamoto, T. On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators. Computing 49, 87–94 (1992). https://doi.org/10.1007/BF02238652

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  • DOI: https://doi.org/10.1007/BF02238652

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