一种求解非线性方程的新算法

A new algorithm for solving the nonlinear equation

针对具有多个根的非线性方程的求解问题提出一种算法 ,将方程转换成一个优化问题 ,利用优化问题的最优值已知这一信息来求解这个优化问题 ,从而达到求解方程的目的 .此算法可以从任意初始点出发收敛到方程的一个根 ,克服了Newton法等要求初始点位于根的附近的缺点 。

An algorithm for solving the nonlinear equation with several solutions is presented. The equation is transformed into an optimization problem. By finding the global minimizers of the optimization problem with the help of the known minimum, the solutions of the equation can be obtained. This algorithm can converge to one of the solutions from any initial point, hence avoid the requirement of Newtons method that the initial point should be near the solutions. Finally, the algorithm is used to solve nonlinear equations.