A modification of Newton method with third-order convergence

• DOI: 10.1016/j.amc.2006.01.076
• Publication Date: 2006-03-24T12:42:37Z
• Authors: Jisheng Kou; Yitian Li; Xiuhua Wang
• Keywords: 0101 mathematics; 01 natural sciences

In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself. Its practical utility is demonstrated by numerical examples.