 A new class of methods with higher order of convergence for solving systems of nonlinear equationsXiaoyong Xiao and Hongwei Yin Applied Mathematics and Computation, 2015, vol. 264, issue C, 300-309 Abstract: By studying the commonness of some fifth order methods modified from third order ones for solving systems of nonlinear equations, we propose a new class of three-step methods of convergence order five by modifying a class of two-step methods with cubic convergence. Next, for a given method of order p ≥ 2 which uses the extended Newton iteration yk = xk − aF′(xk)−1F(xk) as a predictor, a new method of order p + 2 is proposed. For example, we construct a class of m + 2-step methods of convergence order 2m + 3 by introducing only one evaluation of the function to each of the last m steps for any positive integer m. In this paper, we mainly focus on the class of fifth order methods when m = 1. Computational efficiency in the general form is considered. Several examples for numerical tests are given to show the asymptotic behavior and the computational efficiency of these higher order methods. Keywords: Systems of nonlinear equations; Modified Newton method; Order of convergence; Higher order methods; Computational efficiency (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:264:y:2015:i:c:p:300-309 DOI: 10.1016/j.amc.2015.04.094 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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