求解非线性方程的一族预估校正迭代方法

A Family of Predictor Corrector Iteration Methods for Nonlinear Equations

提出一种求解非线性方程f(x)=0问题的一族预估校正迭代方法,证明了该方法是至少三阶收敛的,且在每次迭代过程中,该方法避免求f(x)的二阶导数,减少了运算量.数值实验表明,该迭代方法与其他迭代方法相比具有一定的优势.

We presented a family of predictor corrector iteration methods for solving nonlinear equations,then proved the iteration methods have at least three orders convergence and avoid the computation of the second derivative,and finally tested the methods on several numerical examples.It is observed that our methods can compete with the other classical third-order methods.