Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE CONVERGENCE AND APPLICATIONS OF NEWTON-LIKE METHODS FOR ANALYTIC OPERATORS

  • Published : 2002.09.01

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Abstract

We provide local and semilocal theorems for the convergence of Newton-like methods to a locally unique solution of an equation in a Banach space. The analytic property of the operator involved replaces the usual domain condition for Newton-like methods. In the case of the local results we show that the radius of convergence can be enlarged. A numerical example is given to justify our claim . This observation is important and finds applications in steplength selection in predictor-corrector continuation procedures.

Keywords

References

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