English

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.

Keywords

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

R2 v1 2026-06-22T08:55:44.462Z