论文标题
Steffensen方法的略有概括用于求解非线性方程
A slight generalization of Steffensen Method for Solving Non Linear Equations
论文作者
论文摘要
在本文中，我们提出了一种迭代方法，可以找到非线性方程的简单根，即求解$ f（x）= 0 $的方程。与牛顿的方法不同，我们目的的方法不需要评估衍生物。该方法基于经典的Steffensen方法，它是对其的稍作修改。使用Landau的小o符号和真实分析的概念来表示理论结果的证据。我们证明该方法收敛及其收敛速率是二次的。与给出的数值测试相比，该方法与牛顿和史蒂夫森的方法相比具有一些优势。
In this article, we present an iterative method to find simple roots of nonlinear equations, that is, to solving an equation of the form $f(x) = 0$. Different from Newton's method, the method we purpose do not require evaluation of derivatives. The method is based on the classical Steffensen's method and it is a slight modification of it. The proofs of theoretical results are stated using Landau's Little o notation and simples concepts of Real Analysis. We prove that the method converges and its rate of convergence is quadratic. The method present some advantages when compared with Newton's and Steffesen's methods as ilustrated by numerical tests given.
