Root iterations and the computation of minimum and maximum zeros of polynomials

In this paper, methods which are guaranteed to converge to the minimum or maximum zeros are developed. The proposed methods are based on two approaches for generating fixed point functionsof rational and radical forms. These include well known methods such as the Newton, and Halley methods as special cases, in addition to the rth root methods. Although these methods are only derived for polynomials, they are also applicable to some types of entire functions of finite number of zeros. Additionally, the proposed approach is useful to generate algorithms with any given rate of convergence.