平方收敛公式的一个5阶加速方法

A method of accelerating a quadratically convergent formula to the order of five

为进一步提高收敛阶,文章通过类似Aitken平方加速的加速方法,构造了一个对平方收敛公式的加速方法;在对Newton法使用了该加速方法后,能将2阶的Newton法的收敛速度提高到5阶,并给出了证明;对该5阶迭代公式以预估-迭代的格式写出,计算量将进一步减少,通过实例证实了它的高阶收敛性。

In order to improve the convergence order, this paper presents a new method to accelerate the quadratically convergent formula by using a method similar with the Aithen △^2 Method. It is proved that the order of Newton iterative formula can be increased to fifth when the new method is used. The five-order iterative formula is written in the P-C format,which will contribute to further reducing the amount of calculation,and this is also proved by examples.