Work

Fully computable convergence analysis of a fourth order iterative method for finding polynomial roots

Year: 2025

Type: article

Abstract: This paper investigates the convergence of a fourth-order iterative method for simultaneously finding all roots of a complex polynomial. The method was introduced by Kyurkchiev in 1983 and, in a completely different form, by Zheng and Sun in 1999. To date, only local convergence results are available for this method. In this study, we provide a comprehensive semilocal convergence analysis for the Kyurkchiev-Zheng-Sun method. The resulting theorem includes fully computable initial conditions, a computable a posteriori error estimate, and a localization for each root of the polynomial. The paper concludes with numerical experiments that demonstrate the effectiveness and applicability of the proposed theorem.

Source: Journal of Applied Mathematics and Computing

DOI: 10.1007/s12190-025-02536-7

Authors: Petko D. Proinov, Slav I. Cholakov, Maria T. Vasileva

Institution: Plovdiv University

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: European Commission, NextGenerationEU