Several variations of Newton iteration method

Based on Newton iterative method,three new kinds of iterative methods are constructed in this paper.The first iterative formula(Ⅰ) is a one-step iterative formula.It has second order convergence rate at single root,and needn't evaluate derivative of function.The second iterative formula(Ⅱ) is also one-step iterative formula and has three order convergence at single root.The third iterative formula(Ⅲ) is a two-step iterative formula.There is at least three order convergence rate.Although iterative formula(Ⅲ) is complex,it has advantage of free-computing derivative of function.Moreover,the convergence of three kinds of methods is proved.Finally,some numerical experiments are given,and numerical results are satisfied.