What type of study is this?

September 10, 2025Open Access

An Improved Iterative Scheme for Real and Complex Roots Detection

Key Points

The proposed approach achieves accurate detection of complex roots, even from initial real guesses.
It showcases a notable second-order convergence, quantifying iterations needed for successful resolution.
Efficiency is highlighted through CPU time analysis, alongside the introduction of an efficiency index.
The method employs Python for various numerical experiments, effectively presenting results in both tabular and graphical forms.

Abstract

In this study, researchers propose an innovative numerical approach to solve non-linear equations for real as well as complex roots. The approach, initiated with an initial guess in the complex plane, iteratively converges towards solutions. A notable feature is its ability to accurately identify complex roots even when initialized with a real number. The method demonstrates second-order convergence, with its efficacy evaluated through quantifying the number of iterations needed for convergence. Using Python 3.10.9, experiments were conducted to evaluate its effectiveness across various numerical problems. Results were presented in tabular format, supplemented by graphical representations. Furthermore, the study examines the method's computational efficiency by analyzing CPU time and introducing an efficiency index.

An Improved Iterative Scheme for Real and Complex Roots Detection

Key Points

Abstract

Cite This Study