Banach空间正割法的收敛性

On the convergence of the secant method in Banach space

利用 Hernandez M A等所给的在初始点处的相关信息 ,给出了比 Hernandez M A等较为宽松的正割法收敛条件 ,在得到了类似的误差估计的同时 ,也给出了 ‖ f(xn-1) ‖‖ f (xn)‖ 的误差估计 .

A weaker condition is given for the convergence of the secant method than that in Hernandez M A et al by using the same information at initial points used in Hernandez M A et al. A similar error estimate is also given as that in Hernandez M A et al. At the same time, the error estimate of ‖f(x n+1 )‖‖f(x n)‖ is obtained.