\[ x_{k+1}=x_{k}-f(x_{k})/f'(x_{k}) \] eg.用牛顿迭代法来求解\(x=e^{-x}\)在0.5附近的根

解： \(f(x)=x-e^{-x}\) \(x_{0}=0.5\) \(x_{1}=0.5-(0.5-e^{-0.5})/(1+e^{-0.5})=0.56631\) \(x_{2}=0.56631-(0.56631-e^{-0.56631})/(1+e^{-0.56631})\) · · · \(x_{n}=……\)