First optimal vectorial eighth-order iterative scheme for solving non-linear systems

Alicia Cordero, Juan R. Torregrosa and Paula Triguero-Navarro

Applied Mathematics and Computation, 2025, vol. 498, issue C

Abstract: We introduce a novel iterative method achieving eighth-order convergence, establishing its optimality for solving non-linear systems. A rigorous analysis of convergence order is presented, complemented by investigations into both efficiency indices and the complex dynamics of the proposed method. To assess its performance, extensive numerical experiments are conducted, facilitating comparative analysis with established methods from the literature.

Keywords: Iterative procedures; Non-linear equations and systems; Optimal non-scalar method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:498:y:2025:i:c:s0096300325001286

DOI: 10.1016/j.amc.2025.129401

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