AN ITERATIVE METHOD OF GLOBAL CONVERGENCE WITHOUT DERIVATIVES IN THE CLASS OF SMOOTH FUNCTIONS

In the class of smooth functions, the iterative methods using only first-order derivatives or values of f are established by the idea introducing a parametric function and making the global estimate for the interpolating remainder. These methods are globally convergent and contain a real parameter lambda (greater-than-or-equal-to 0). When 0 less-than-or-equal-to lambda less-than-or-equal-to 1, the order of convergence of the methods is 1 + lambda for a simple real zero of f(x), and 1 for a multiple real zero. When 1 < lambda, these methods are only linearly convergent for any real zero of f(x).