含参无导数有记忆迭代方法与其动力系统的构造

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

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.