摘要
借鉴含导数两步迭代格式转化成不含导数两步迭代格式的思想,提出了一种更通用的两步无导数迭代格式,通过权值保证了两步无导迭代格式达到最优阶;利用自加速参数和Newton(牛顿)插值多项式得到了两参和三参有记忆迭代格式,并与已有的两参和三参有记忆迭代格式进行比较;给出了几个格式的吸引域,比较了几个迭代格式的性能.
According to the usual practice that 2-step iterative methods with derivative are transformed into derivative-free schemes,a more general 2-step derivative-free iterative method was proposed. For this method the optimal order of convergence was ensured by the weight value. By means of the self-accelerating parameter and the Newton interpolation polynomial, the 2-parameter and 3-parameter iterative schemes with memory were obtained. Some of the existing 2-and 3-parameter iterative methods with memory were compared with the proposed method. The attraction domains of several schemes were presented,and the performances of several iterative schemes were compared.
出处
《应用数学和力学》
CSCD
北大核心
2017年第12期1342-1358,共17页
Applied Mathematics and Mechanics
基金
国家自然科学基金(61272024)~~
关键词
非线性方程
收敛阶
有记忆和无记忆方法
无导数
自加速参数
non-linear equation
order of convergence
method with or without memory
de-rivative-free
self-accelerating parameter