解非线性方程的一类三阶迭代公式

A Class of Cubic Convergence Iteration Formulae for Solving a Nonlinear Equation

在牛顿迭代公式的基础上,给出一类新的迭代公式,既克服了牛顿迭代法中分母可能为零的缺点,又保证了该类公式至少是三阶收敛的.并通过几个数值算例验证了该类方法的有效性.

On the basis of the Newton iteration formula, a new iterative scheme is given, which can save the denominator from zero that may occur in the dominator in Newton iterative method, and can guarantee the formula to be cubic convergent. Several numerical examples are presented to illustrate the effectiveness of our method.