一族带有参数的三阶收敛迭代方法

A family of third-order convergence iterative method with parameters

根据经典牛顿法和Runge-Kutta方法的思想,文章提出了解非线性方程f(x)=0近似解的一族带有参数的迭代方法,即通过设定不同的参数值,从而得到不同的迭代方法。经收敛性分析和证明,得出该族方法都至少三阶收敛到单根,目前一些已知改进的牛顿迭代法都是该族方法中的特殊情况。最后用数值试验证明了该方法与同阶收敛性质方法相比具有一定的有效性。

According to the Newton＇ s method and Runge-Kutta method, this paper puts forward an it- erative method with parameters for solving the approximate solution of nonlinear equations f（x）=0. By setting different parameter values, different iterative methods can be gotten. Through the conver- gence analysis and proof, it is known that the method is at least convergent to simple root of third or- der. Some existing improved Newton iterative methods are the special cases of this method. Finally, the results of numerical experiments show that this method has effectiveness compared with other third-order iterative methods.