条件最优的两步迭代法及Jarratt变形方法

A conditional optimal two-step iterative method and a variant of Jarratt method

以y_n=x_n-θf(x_n)/f'(x_n)(0<θ≤1)为基础,构造了一类新的带有参数的条件最优的两步迭代方法,其收敛阶数可达到四阶,且符合Kung-Traub猜想(n=3情形).另外,该方法包含了一些已有的迭代法,尤其包含了Jarratt方法.数值验证表明,本文方法优于牛顿迭代法及一些已有的方法,具有较好的有效性和可行性.

Based on yn=xn-θf（xn）/f＇（xn）（0θ≤1）,a new conditional optimal two-step iterative method with one-parameter for solving nonlinear equations is presented.The order of convergence arrives to at least four and agrees with the conjecture of Kung-Traub for the case n=3.Moreover,this method contains some existing methods especially contains the Jarratt method.Several numerical results are shown that this method is surperior to Newton＇s method and other existing methods.Therefore our method is more efficient and performs better than other methods.