Construction of zero-finding methods by Weierstrass functions

In this paper, we present a simple and elegant procedure for the construction of iterative methods for the simultaneous determination of (simple or multiple) zeros of an algebraic polynomial. This procedure is based on the application of a special type of functions, called Weierstrass’ functions, to suitable zero-finding methods for a single zero. For demonstration, using this approach we derive many known iterative methods in a simpler way compared with original derivations, as well as some new methods. Aside from the presented methodology in developing zero-finding methods, the paper offers a short review of simultaneous methods including some historical notes.