Complexity of an homotopy method at the neighbourhood of a zero
- Yakoubsohn, J.-C. 3
- Gutiérrez, J.M. 1
- Magreñán, Á.A. 2
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1
Universidad de La Rioja
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2
Universidad Internacional de La Rioja
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3
Paul Sabatier University
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Publisher: Springer
ISBN: 978-3-319-39227-1
Year of publication: 2016
Volume: 10
Pages: 147-171
Type: Book chapter
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Abstract
This paper deals with the enlargement of the region of convergence of Newton’s method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered function. The novelty in our approach is the establishment of new convergence results based on a Lipschitz condition with a L-average for the involved operator. In particular, semilocal convergence results (Kantorovich-type results), as well as local convergence results (γ-theory) are obtained. © Springer International Publishing Switzerland 2016.