Enlarging the domain of starting points for Newton's method under center conditions on the first Fréchet-derivative
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Universidad de La Rioja
info
ISSN: 0885-064X
Year of publication: 2016
Volume: 33
Pages: 89-106
Type: Article
More publications in: Journal of Complexity
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Abstract
We analyze the semilocal convergence of Newton's method under center conditions on the first Fréchet-derivative of the operator involved. We see that we can extend the known results so far, since we provide different starting points from the point where the first Fréchet-derivative is centered (that is the situation usually considered by other authors), so that the domain of starting points is enlarged for Newton's method. We also illustrate the theoretical results obtained with some mildly nonlinear elliptic equations. © 2015 Elsevier Inc. All rights reserved.