具有参数平方收敛的线性插值迭代类

A Class of Parametric Linear Interpolation Iterative Methods with Quadratic Convergence

提出了一类具有参数平方收敛的求解非线性方程的线性插值迭代法,方法以Newton法和Steffensen法为其特例,并且给出了该类方法的最佳迭代参数.数值试验表明,选用最佳迭代参数或其近似值的新方法比Newton法和Steffensen方法更有效.

We develop a class of parametric linear interpolation iterative methods with quadratic convergence to solve nonlinear equations, inclusing Newton＇s Method and Steffensen method, and give their optimum iterative parameter. The numerical experiments show that new methods with optimum iterative parameter or its approximate value are effective and comparable to well-know methods of Newton and Steffensen.