The cubic semilocal convergence on two variants of Newton's method
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摘要
In this paper, we discuss two variants of Newton's method without using any second derivative for solving nonlinear equations. By using the majorant function and confirming the majorant sequences, we obtain the cubic semilocal convergence and the error estimation in the Kantorovich-type theorems. The numerical examples are presented to support the usefulness and significance.
论文关键词：Nonlinear equation,Newton's method,Cubic semilocal convergence
论文评审过程：Received 17 November 2006, Revised 12 March 2007, Available online 12 September 2007.
论文官网地址：https://doi.org/10.1016/j.cam.2007.09.003
