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

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.

44 pages; keywords: iterative methods, cone metric space, convergence analysis, error estimates, Weierstrass method, polynomial zeros

References in corpus (1)

• A unified theory of cone metric spaces and its applications to the fixed point theory

Cited by in corpus (1)

• On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously