求解非线性方程重根的二阶迭代法

A second-order iterative method for extracting multiple roots of nonlinear equations

考虑非线性方程的求根问题,将非线性方程问题转化为求函数极值问题.利用无约束优化技术中的牛顿法,对于单根,得到的算法与New-Raphson求根算法等价;对于重根,在不计算二阶导数的情况下,给出了具有二阶收敛速度的求根算法.

This paper concerns the problem of solving nonlinear equations. It is shown that solving nonlinear equations is equivalent to finding out the extremum of function. Applying Newton method of unconstrained optimization technology, the algorithm we have obtained for single root is equivalence to New-Raphson＇s algorithm;and for multiple roots, the root-extracting algorithm having second-order convergence rate is proposed without calculating 2-order derivatives.