Extended and unified local convergence for Newton-Kantorovich method under w- conditions with applications
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Date
2017
Authors
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Journal ISSN
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Publisher
World Scientific and Engineering Academy and Society mastorakis4567@gmail.com Ag. Ioannou Theologou 17-23, Zographou Athens 15773
Abstract
The goal of this paper is to present a local convergence analysis of Newton's method for approximating a locally unique solution of an equation in a Banach space setting. Using the gauge function theory and our new idea of restricted convergence regions we present an extended and unified convergence theory.
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Keywords
Banach space, Convergence region, Gauge function, Newton's method, Newton-Kantorovich theorem, Semilocal convergence
Citation
WSEAS Transactions on Mathematics, 2017, 16, , pp. 248-256