| 含参无导数有记忆迭代方法与其动力系统的构造 |
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| 引用本文： | 王婷,唐烁.含参无导数有记忆迭代方法与其动力系统的构造[J].应用数学和力学,2017,38(12):1342-1358. |
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| 作者姓名： | 王婷 唐烁 |
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| 作者单位： | 合肥工业大学 数学学院, 合肥 230009 |
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| 基金项目： | 国家自然科学基金（61272024） |
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| 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.
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| 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 |
| 收稿时间： | 2016-11-14 |
Construction of a Parametric Derivative-Free Iterative Method With Memory for Dynamic System Analysis |
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| Affiliation: | School of Mathematics, Hefei University of Technology, Hefei 230009, P.R.China |
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| 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. |
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