牛顿迭代收敛的加速

基于Newton迭代法单根的二阶收敛性和重根的线性收敛性,提出了加速牛顿迭代收敛的思想。利用反函数的性质,取Taylor展开式的前三项进行迭代;并利用差商代替导数的方法,构造出更高收敛阶的迭代公式。大量的数值实验结果表明,本文算法理论上的推导是完全可行的,且有效地提高了迭代公式的收敛速度。

The Acceleration of Convergence of Newton' s Iterative

Based on second - order convergence of simple root and first - order convergence of the heavy root of Newton iterative, This paper proposes a new idea for accelerating the convergence of Newton' s method This method is to utilize nature of inverse function, the first three which fetch the type that launches Taylor change taking the place of, Divided difference has appeared at the same time to replace a steps of derivatives, and constructs a kind of third - order convergence Newton' s iterative schemes. Indicate through a large amount of number value experimental results , deriving in theory is totally feasible, and has improved the speed of convergence which takes the place of the form of changing greatly .