Convergence of a Family of Accelerated Schröder-like Methods for the Simultaneous Extraction of Simple and Multiple Polynomial Zeros
Year: 2026
Type: article
Abstract: In the present paper, we investigate the local and the semilocal convergence of a recently constructed family of accelerated simultaneous methods with two corrections applied to polynomials with simple and multiple zeros. A new local convergence theorem that provides explicit domains of initial conditions and error estimates ensuring the Q-convergence of the methods from the first iteration is established. Based on this result, we derive a semilocal convergence theorem, for simple zeros, with computable initial conditions and an error estimate, making it directly applicable in practice. Three numerical tests illustrate the applicability of the theoretical results.
Source: Axioms
Authors: Ivan Ginchev, Stoil I. Ivanov, Boyan Zlatanov
Institution: Plovdiv University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7216170283