Volume 7, Issue 3
Semilocal Convergence Theorem for a Newton-like Method

East Asian J. Appl. Math., 7 (2017), pp. 482-494.

Published online: 2018-02

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• Abstract

The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.

• Keywords

Newton-like method, nonlinear equation, Newton-Kantorovich theorem, γ-condition, error estimate.

65F10, 65F50, 65H10

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@Article{EAJAM-7-482, author = {}, title = {Semilocal Convergence Theorem for a Newton-like Method}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {3}, pages = {482--494}, abstract = {

The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090816.270317a}, url = {http://global-sci.org/intro/article_detail/eajam/10760.html} }
TY - JOUR T1 - Semilocal Convergence Theorem for a Newton-like Method JO - East Asian Journal on Applied Mathematics VL - 3 SP - 482 EP - 494 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.090816.270317a UR - https://global-sci.org/intro/article_detail/eajam/10760.html KW - Newton-like method, nonlinear equation, Newton-Kantorovich theorem, γ-condition, error estimate. AB -

The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.

Rong-Fei Lin, Qing-Biao Wu, Min-Hong Chen, Lu Liu & Ping-Fei Dai. (2020). Semilocal Convergence Theorem for a Newton-like Method. East Asian Journal on Applied Mathematics. 7 (3). 482-494. doi:10.4208/eajam.090816.270317a
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