Some variants of Cauchy's method with accelerated fourth-order convergence

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摘要

In this paper, we present some variants of Cauchy's method for solving non-linear equations. Analysis of convergence shows that the methods have fourth-order convergence. Per iteration the new methods cost almost the same as Cauchy's method. Numerical results show that the methods can compete with Cauchy's method.

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

论文评审过程：Received 12 July 2006, Revised 31 December 2006, Available online 21 February 2007.

论文官网地址：https://doi.org/10.1016/j.cam.2007.01.031