求重根的一类三阶迭代法

A family of multiple root finding methods with cubical convergence

给出了求非线性方程重根的一类迭代法,证明了这类方法的三阶收敛性,获得了迭代误差,指出了这个类的广泛性,即它包含了一些已知的方法.通过数值例子与一些已知方法进行比较,说明了新方法的有效性,即在某些情形下,新方法比一些已知方法收敛快,且在其他方法发散的情况下新方法还是以很快的速度收敛.

A new family of iterative methods to find multiple roots of a nonlinear equation was obtained. Third order convergence was proved for these methods and iteration errors were given. The generality of the family was presented: the family includes,as particular cases,several well known families and methods. By comparing the proposed methods with some other methods through numerical experiments,the robustness and efficiency of the new methods were shown. It was showed that the presented methods converge faster than some other methods and even converge very fast at some cases while the other methods diverge.