同时求解非线性代数方程全部根的Newton迭代法

Newton Iterative Method for Simultaneous Finding all Roots of a Nonlinear Algebraic Equation

讨论同时求解非线性代数方程全部根的Newton迭代解法及其收敛性。给出了保证该迭代法收敛的初始值的一个范围。 从证明过程可见该迭代法适用于求解非线性代数方程的全部单复根。数值例子的结果是满意的。

This paper discusses the convergence of Newton iterative method for simultaneous finding all roots of a nonlinear algebraic equation . For appropriately chosen starting values, it is proved that the method is convergent and the convergence order is at least 2. The proof of convergence showed that the Newton method can be used for finding simple real or complex roots. The numerical results are satisfactory.