牛顿混沌迭代法及其在电机中的应用

电机中的许多问题都可以转化为非线性方程组的求解问题,牛顿迭代法是重要的一维及多维的迭代技术,其迭代本身对初始点非常敏感,该敏感区是牛顿迭代法所构成的非线性离散动力系统Ju lia集。本文提出了用排斥二周期点寻找牛顿迭代函数的Ju lia点的求解方法,利用非线性离散系统在其Ju ilia集出现混沌分形现象的特点,首次提出了基于混沌的牛顿迭代的非线性方程组求解的新方法。计算实例表明了该方法的正确性与有效性。

Newton Chaos Iterative Method and Its Application in Electric Machine

Many questions in electric machine studies can be expressed with a set of nonlinear equations.Newton iterative method is an important technique for calculating one dimensional or multidimensional variable.A nonlinear discrete dynamic process is sensitive to initial guess point,which shows a fractal nature.The sensitive area of Newton method is called Julia set that is composed of the boundary of attractive region,and it reveals complex fractal structure and chaos phenomena.By constructing repulsion two-cycle point function and adopting inverse image iterative method,a way to determine Julia set point is introduced.On the basis of that,a new approach based on Julia set is proposed for solving nonlinear equations.Some features of fractal are employed in the method.The numerical examples show that the method is effective.