New eighth-order iterative methods for solving nonlinear equations

作者：Wang Xia; Liu Liping^*

来源：Journal of Computational and Applied Mathematics, 2010, 234(5): 1611-1620.

DOI：10.1016/j.cam.2010.03.002

• Nonlinear equations
• Iterative methods
• Weight function methods
• Convergence order
• Efficiency index

In this paper, three new families of eighth-order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods. Per iteration these iterative methods require three evaluations of the function and one evaluation of the first derivative. This implies that the efficiency index of the developed methods is 1.682, which is optimal according to Kung and Traub's conjecture [7] for four function evaluations per iteration. Notice that Bi et al.'s method in [2] and [3] are special cases of the developed families of methods. In this study, several new examples of eighth-order methods with efficiency index 1.682 are provided after the development of each family of methods. Numerical comparisons are made with several other existing methods to show the performance of the presented methods. Published by Elsevier B.V.

• 出版日期2010-7-1
• 单位郑州轻工业大学