Some modifications of Newton's method with fifth-order convergence

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摘要

In this paper, we present some new modifications of Newton's method for solving non-linear equations. Analysis of convergence shows that these methods have order of convergence five. Numerical tests verifying the theory are given and based on these methods, a class of new multistep iterations is developed.

论文关键词：41A25,65D99,Newton's method,Non-linear equations,Iterative method,Root-finding

论文评审过程：Received 15 May 2006, Revised 21 July 2006, Available online 30 November 2006.

论文官网地址：https://doi.org/10.1016/j.cam.2006.10.072