函数方程求根的一种新型大范围收敛迭代法

1引言实际解函数方程f(x)=0(z∈α,β],f(α)f(β)＜0,f(x~*)=0)时,人们常常希望选用那些仅计算函数值,具有大范围收敛性且效率较高的方法,特别对那些表示式复杂的函数以及病态函数．例如,那种仅在的某个充分小邻域内连续,而在该邻域之外光滑性很差的函数；那种在初始含根区间(α,β)上起伏多变的函数；那种|f(α)|和|f(β)|差别甚大,而x~*又十分靠近绝对值较大者一端的函数等等,这种欲望就更加强烈．

A NEW TYPE OF GLOBALLY CONVERGENT ITERATION METHOD FOR FINDING ROOTS OF FUNCTIONAL EQUATION

This paper presents a new type of globally convergent iteration method for finding roots of functional equation f(z)=0.The parameter of an iteration, which is selected dynamically according to the computation process,is contained in the method.A good selection for it can make the method having very repaid con- vergence rate.One function value is computed in an iteration step of the method, and what the convergence of it requires for function f(x)is the same as that of the bisection method.Therefore,the iteration method is of excellent universal suitability and efficiency.