艾特肯式方法效率高

IF 0.4 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute Pub Date : 2018-08-01 DOI:10.1016/j.trmi.2018.01.001

Pankaj Jain, Kriti Sethi

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引用次数: 4

摘要

本文研究了求解非线性方程的Aitken型迭代法，其中插值节点由牛顿法的变体或p阶的一般方法控制，并与广义割线法相结合，证明了该方法的收敛阶可以提高到期望的高度，并且在极限情况下，该方法的效率为2。给出了几个数值算例来支持理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Aitken type methods with high efficiency

In this paper, we study the iterative method of Aitken type for solving the non-linear equations, in which the interpolation nodes are controlled by variant of Newton method or by a general method of order $p .$ By combining such methods with a generalized secant method, it is shown that the order of convergence can be increased to as high as desired and also in the limiting case efficiency of the method is 2. Several numerical examples are provided in support of the theoretical results.

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来源期刊

Transactions of A Razmadze Mathematical Institute MATHEMATICS-

CiteScore

0.50

自引率

50.00%

发文量

审稿时长

22 weeks