On the convergence of Gander’s type family of iterative methods for simultaneous approximation of polynomial zeros

Petko D. Proinov, Stoil I. Ivanov and Miodrag S. Petković

Applied Mathematics and Computation, 2019, vol. 349, issue C, 168-183

Abstract: In this paper, we propose a fifth-order family of iterative methods for approximation of all zeros of a polynomial simultaneously. The new family is developed by combining Gander’s third-order family of iterative methods with the second-order Weierstrass root-finding method. The aim of the paper is to state initial conditions that provide local and semilocal convergence of the proposed methods as well as a priori and a posteriori error estimates. In the case of semilocal convergence the initial conditions and error estimates are computationally verifiable which is of practical importance.

Keywords: Polynomial zeros; Iteration methods; Simultaneous methods; Local convergence; Semilocal convergence; Error estimates (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:349:y:2019:i:c:p:168-183

DOI: 10.1016/j.amc.2018.12.041

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