一族带有两参数的修正型Chebyshev-Halley迭代方法（英文）

A two-parameter family of modified Chebyshev-Halley methods

应用(2,1)阶Padé逼近方法,得到不需要计算二阶导数求解非线性方程的修正型Chebyshev-Halley方法的新两参数族,证明该族方法是至少三阶收敛。该族方法的每步迭代需要计算两个函数和一个一阶导数,数值实验表明,该族迭代方法与其它方法相比,在许多方面得到了更好的数值结果。

A new two-parameter family of modified Chebyshev-Halley methods free from second derivative is obtained by using the second degree Pade approximant. It is shown that the proposed methods have convergence order three or higher. The family of methods requires two functions and one first derivative e- valuation per iteration. Numerical examples are given to illustrate that the proposed methods are competitive with some other well known existing methods and give better numerical results in many aspects.