General convergence theorems for iterative processes and applications to the Weierstrass root-finding method
Numerical Analysis
2015-03-19 v1 Functional Analysis
Abstract
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.
Cite
@article{arxiv.1503.05243,
title = {General convergence theorems for iterative processes and applications to the Weierstrass root-finding method},
author = {Petko D. Proinov},
journal= {arXiv preprint arXiv:1503.05243},
year = {2015}
}
Comments
44 pages; keywords: iterative methods, cone metric space, convergence analysis, error estimates, Weierstrass method, polynomial zeros