对牛顿类方法的讨论

Study on Newton-like Method

对解非线性和超越方程f(x)=0的"牛顿类"方法xn+1=xn-f(xn)/(αf(xn)+f′(xn))作了进一步的分析,认为参数α的取值范围直接影响公式的收敛速度,从而给出了α取值的依赖性条件,并给出了加速算法和数值算例.

For the ＂Newton-like＂ method xn＋1=xn-f（xn）/（αf（xn）＋f′（xn）） of solving nonlinear and transcendental equation f（x）=0,a further analysis is proposed in this paper.The analysis indicates that the range of parameter α directly affects the convergence rate of the formula.Hence,the dependent conditions of α are given here.The accelerated algorithm and the numerical examples are also presented.