对牛顿迭代法条件的一个改进  

An Improvement on Conditions of the Newton′s Iteration Method

作　　者：肖光强[1,2] 方壮[3] 余显志[2] 

机构地区：[1]重庆大学数理学院,重庆400030 [2]后勤工程学院基础部,重庆400016 [3]湖北民族学院理学院,湖北恩施445000

出　　处：《湖北民族学院学报（自然科学版）》2008年第4期395-397,共3页Journal of Hubei Minzu University(Natural Science Edition)

摘　　要：对解非线性和超越方程f(x)=0的牛顿迭代法的收敛条件作了改进,并证明在此条件下二阶收敛性仍成立,得到较简洁的判定运用牛顿法求近似根的条件及比值收敛因子,并给出了数值实验.The convergence condition of Newton iteration method for the solution of nonlinear and transcendental equations f（x） = 0 is improved, and the second order convergence is proved under this condition. A more concise condition for determining approximate root by the use of Newtons method and the ratio of Convergence factor are obtained, and also the numerical experiments is given.

关 键 词：牛顿迭代法 二阶收敛性 LIPSCHITZ条件 

分 类 号：O241.7[理学—计算数学]