Semilocal convergence of a family of multi-point ehrlich-type root-finding methods

In this talk, we discuss the convergence of a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a polynomial simultaneously. The purpose of the talk is to present a convergence theorem for the multi-point Ehrlich-type methods with computationally verifiable initial conditions. The new result is obtained by using a new approach to the iteration functions of multi-point simultaneous methods developed recently in [1] as well as by using an initial condition conversion theorem of Proinov [2].