一类新型牛顿迭代的效率研究

Study on the Efficiency of a New Kind of Newton Iteration

主要利用反函数插值技巧构造了多节点Hermite型牛顿迭代格式,获得了多节点Hermite型牛顿迭代法的收敛阶所满足的方程,证明了其收敛阶随着节点个数的增加而严格单调递增并趋近于3,接着利用效率指数作为判据,给出了在不同的计算量下,多节点Hermite型牛顿迭代法所需的最优节点数,最后进行了数值验证.

In this paper,the multi node Hermite deformed Newton iterative scheme is con-structed by using the inverse interpolation technique,the equation satisfied by the convergence order of the multi node Hermite Newton method in the general form is obtained,and the con-vergence order of the multi node Hermite Newton method is proved,which increases strictly monotonically with the increase of the number of nodes and approaches 3.Then,the efficiency index is used as the criterion,and the corresponding optimal iterative scheme of Hermitian Newton method under different computational quantities are given.Finally,numerical verifi-cations are carried out.