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

Rong-Fei Lin, Qing-Biao Wu, Min-Hong Chen, Lu Liu & Ping-Fei Dai

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.

  • AMS Subject Headings

65F10, 65F50, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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