一族解非线性方程的带参数Steffensen型三阶方法及其高阶变形

A family of cubically Steffensen-like methods with parameters for solving nonlinear equations and its higher-order variants

摘要: 针对非线性方程的求解问题,利用差分代替导数,构造出了一族带有2个参数的Steffensen型方法.该方法不仅避免了求导数运算,而且通过调节参数,可以提高收敛阶数,是Steffensen法的一种改进.通过数值算例对本文算法与Newton法、Steffensen法进行比较,算例显示本文所给算法是可行的和有效的.

Abstract: Replacing derivative by difference quotient and introducing two parameters,a family of Steffensen-like methods for solving nonlinear equations is proposed.The methods not only avoid the derivative,but also can improve the order of convergence by adjusting the parameters,they are improved Steffensen methods.A few examples are given to compare with the Newton method and Steffensen method.The examples show that the methods are feasible and effective.