A New Family of Fourth-Order Optimal Iterative Schemes and Remark on Kung and Traub’s Conjecture

Chein-Shan Liu, Tsung-Lin Lee and Xiaolong Qin

Journal of Mathematics, 2021, vol. 2021, 1-9

Abstract: Kung and Traub conjectured that a multipoint iterative scheme without memory based on m evaluations of functions has an optimal convergence order p=2m−1. In the paper, we first prove that the two-step fourth-order optimal iterative schemes of the same class have a common feature including a same term in the error equations, resorting on the conjecture of Kung and Traub. Based on the error equations, we derive a constantly weighting algorithm obtained from the combination of two iterative schemes, which converges faster than the departed ones. Then, a new family of fourth-order optimal iterative schemes is developed by using a new weight function technique, which needs three evaluations of functions and whose convergence order is proved to be p=23−1=4.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5516694

DOI: 10.1155/2021/5516694

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