Two Iterative Methods with Memory Constructed by the Method of Inverse Interpolation and Their Dynamics

Mathematics

Mingming Zhu¹  Xiaofeng Wang¹ 

[1] School of Mathematical Sciences, Bohai University, Jinzhou 121000, China;

关键词: multipoint iterative methods;    with memory;    nonlinear equations;    inverse interpolation;    root-finding;   

DOI  :  10.3390/math8071080

来源: DOAJ

【 摘 要 】

In this paper, we obtain two iterative methods with memory by using inverse interpolation. Firstly, using three function evaluations, we present a two-step iterative method with memory, which has the convergence order 4.5616. Secondly, a three-step iterative method of order 10.1311 is obtained, which requires four function evaluations per iteration. Herzberger’s matrix method is used to prove the convergence order of new methods. Finally, numerical comparisons are made with some known methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the presented methods.

【 授权许可】

Unknown