On a family of Weierstrass-type root-finding methods with accelerated convergence

Kyurkchiev and Andreev (1935) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of this sequence of iterative methods is the famous method of Weierstrass (1891) and the second one is the method of Nourein (1977). For a given integer N >= 1, the Nth method of this family has the order of convergence N + 1. Currently in the literature, there are only local convergence results for these methods. The main purpose of this paper is to present semilocal convergence results for the Weierstrass-type methods under computationally verifiable initial conditions and with computationally verifiable a posteriori error estimates. (C) 2015 Elsevier Inc. All rights reserved.