一个超平方收敛的迭代公式及其加速

An Iterative Formula with Super-quadratic Convergence and its Acceleration

借助于函数y=f(x)的反函数x=φ(y)的Hermite三次插值多项式,给出了一个迭代公式,证明了它是超平方收敛的。并应用Steffensen加速法,得到了一个单步法迭代公式,证明了它是至少四阶收敛的。最后,通过与牛顿法公式比较的数值实验,证明了公式及加速的有效性。

In this paper, using＇s inverse function＇s third order Hermite int we give an iterative formula, and prove it is super-quadratic convergence. Then using Steffense accelerated method, we gain a single step method iterative formula, and prove its convergent order is at least four. Last, through comparing the result of the numerical experiment with Newton iterative methods, we can show the formula and acceleration is effective.