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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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