Convergence analysis for a deformed Newton's method with third-order in Banach space under γ-condition

Authors:
Yueqing Zhao;Qingbiao Wu
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China,Department of Mathematics, Taizhou University, Linhai, Zhejiang, People's Republic of China;Department of Mathematics, Taizhou University, Linhai, Zhejiang, People's Republic of China
Venue:
International Journal of Computer Mathematics
Year:
2009

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Abstract

We establish the Newton-Kantorovich convergence theorem for a deformed Newton's method in Banach space under γ-condition, which is used to solve the nonlinear equation. We also present the error estimate. Finally, some examples are provided to show the application of our theorem.