General convergence theorems for iterative processes and applications to the Weierstrass root-finding method

摘要

In this paper, we prove some general convergence theorems for the Picard iteration in cone metric spaces over a solid vector space. As an application, we provide a detailed convergence analysis of the Weierstrass iterative method for computing all zeros of a polynomial simultaneously. These results improve and generalize existing ones in the literature. (C) 2015 Elsevier Inc. All rights reserved.