含参无导数有记忆迭代方法与其动力系统的构造

王婷; 唐烁

doi:10.21656/1000-0887.370350

含参无导数有记忆迭代方法与其动力系统的构造

doi: 10.21656/1000-0887.370350

王婷,
唐烁

合肥工业大学数学学院, 合肥 230009

基金项目: 国家自然科学基金（61272024）

详细信息

作者简介:
王婷（1991—），女，硕士（通讯作者. E-mail: 503669777@qq.com）;唐烁（1964—），男，教授，硕士生导师.

中图分类号: O241.7
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- 被引次数: 0
出版历程
- 收稿日期: 2016-11-14
- 修回日期: 2017-10-16
- 刊出日期: 2017-12-15

Construction of a Parametric Derivative-Free Iterative Method With Memory for Dynamic System Analysis

School of Mathematics, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The National Natural Science Foundation of China(61272024)

摘要

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.
- 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
Abstract: 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.
- non-linear equation /
- order of convergence /
- method with or without memory /
- derivative-free /
- self-accelerating parameter

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参考文献(17)

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