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.
翻译:在本篇文章中,我们提出了一个迭接方法来寻找非线性方程的简单根根,即解决美元(x)=0美元的方程。不同于牛顿的方法,我们的目的方法并不要求评估衍生物。该方法以古典Stefdefent的方法为基础,是对它略作修改。理论结果的证明用Landau的“小笔记”和“真实分析”的简单概念来说明。我们证明该方法的趋同及其趋同率是四面形的。与牛顿和Steffesen的方法相比,该方法具有一定的优势,因为给出的数值测试将这两个方法加以解释。