用于求根问题的一个基于Thiele连分式的四阶收敛的迭代方法

A Fourth-Order Convergent Iterative Method by Means of Thiele's Continued Fraction for Root-Finding Problem

中文关键词:  非线性方程  Thiele连分式  Viscovatov算法  迭代方法  收敛阶数

英文关键词:non-linear equation  Thiele's continued fraction  Viscovatov algorithm  iterative method  order of convergence

中文摘要:

      利用截断的Thiele连分式,本文给出了一个求解非线性单变量方程的单步迭代方法,并证明了所提出的迭代方法具有四阶收敛性.最后,本文通过一些数值例子说明了所提出的方法的有效性和表现.

英文摘要:

      In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.