On some simultaneous methods based on Weierstrassʹ correction

The purpose of the paper is to present some procedures for the construction of simultaneous methods for finding all zeros of a polynomial f using Weierstrassʹ corrections Wi(z) = f(z)∏k≠i(z−zk). In this manner some well-known methods as well as new methods are obtained. The proposed iterative algorithms are realized in ordinary complex arithmetic and circular interval arithmetic. The convergence analysis of the presented methods and numerical examples are given.