解非线性方程的一类改进型牛顿法

An Improved Newton Method for Solving Nonlinear Equation

牛顿迭代法的改进形式主要有算术平均牛顿法(AN)、几何平均牛顿法(GN)、中点牛顿法(MN)、调和平均牛顿法(HN)、α-幂平均牛顿法(PN)等.通过将算术平均牛顿法(AN)与经典牛顿法结合,提出一种新的牛顿型算法,收敛阶可达6阶.与现有算法相比较,该算法具有计算量少、收敛速度快的优点.

Newton iterative method is a classical algorithm for solving nonlinear equations.In recent years,there have been many of its improved forms,such as the arithmetic average method of Newton(AN),the harmonic mean method of Newton(HN),geometric mean Newton method(GN),alpha power mean Newton method(PN),and middle point Newton method(MN)and so on.In this paper,combined with the classical Newton method and the arithmetic mean of the Newton method(AN),a new Newton type algorithm is presented,which can achieve six order convergences.Compared with the existing algorithms,this algorithm has the advantages of less computation and fast convergence speed.