一个比Newton法收敛快而稳的两点切线法

Tangential methos at two points having more accelerating and stable convergence than Newton method

重复使用迭代信息反插值构造逆函数的近似，一方面较只使用单点信息能更好地逼近隐式函数，另一方面直接得到显式近似解．于是，得到了逼近精度高、计算速度快、表达简单的迭代格式．这就是在一元方程的求根和一维搜索中综合了切线法和割线法的新方法，并且获得收敛快而稳的满意结果；称为两点切线法．

Reusing iterative information ,an approximate inverse function is constructed byinverse interpolation. The approximation approaches to original implicit function are more closethan approximate functions using information at single point.Authors can immediately getexplicit approximate solution instead of solving the approximation of the original function.Thereby,a new method is obtained in finding roots of one variable’s equation and looking foroptimum solutions of one dimensional search.It has higher accuracy approaching to originalfunction , accelerating calculation and simple iterative pattern. Because the method,named astangential method at two points,synthesizes tangential method and secant method, it can getsatisfactory computational results of accelerating and stable convergence.