几类改进的新的两步六阶Chebyshev-Halley方法

New Families of Modified Two-Step Chebyshev-Halley Methods with Sixth-Order Convergence

利用权函数法,给出非线性方程求根的Chebyshev-Halley方法的几类改进方法,证明方法六阶收敛到单根.Chebyshev-Halley方法的效率指数为1.442,改进后的两步方法的效率指数为1.565.最后给出数值试验,且与牛顿法,Chebyshev-Halley方法及其它已知的方程求根方法做了比较.结果表明方法具有一定的优越性.

Applying the method of weight functions,new families of improvements of ChebyshevHalley methods are given.The convergence property is proved and the present methods converge to the simple roots with sixth-order.The efficiency index of Chebyshev-Halley methods is 1.442 and the modified two-step Chebyshev-Halley methods＇ is 1.565.In the end,numerical tests are given and the present methods are compared with Newton＇s method,ChebyshevHalley methods and other known root-finding methods.The results show that the proposed methods have some more advantages than other methods.