基于一致系数求积的广义牛顿法求解非线性方程组

Uniform-coefficient Quadrature-based Iterative Methods for Solving Nonlinear Equations

采用一致系数求积公式近似逼近泰勒余项,得到一种新的求解非线性方程组的广义牛顿法.给出算法的一般形式,证明算法是三阶收敛的,并且在一定的温和条件下可以达到五阶收敛.最后,给出数值例子说明算法的有效性和稳定性.

In this paper,we present a new variant of Newton＇s method for solving nonlinear equations based on uniform-coefficient quadrature formulas.The cubic convergence of the proposed algorithm is established.Moreover,the fifth-order convergence is proved under some mild conditions.Some numerical experiments are reported to illustrate the effectiveness and the flexibility of our algorithm.