Application of Search Algorithms to Root-Finding Problems in Algebraic and Transcendental Contexts

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6351

Keywords:

Root-finding algorithms, Optimization, Binary search algorithm, Golden ratio search algorithm, Fibonacci search algorithm

Abstract

In this study, bisection algorithm, golden ratio and Fibonacci search algorithms are used to find the roots of univariate, logarithmic, trigonometric, exponential and polynomial functions. The results obtained from these methods are compared, and the fundamental principles, advantages, and disadvantages of each algorithm are discussed in terms of numerical stability. The approximation to the root with minimal error and the fewest steps is analyzed. The study concludes with results and recommendations based on comparative analysis.

Author Biographies

  • Bayram Köse, Izmir Bakırçay University

    Bayram Köse  is currently a Full Assistant Professor at the department of the Electric Electronic Engineering of Izmir Bakırçay University, Izmir, Turkey. He obtained his Ph.D. degree in Energy Systems Engineering from the Institute of Science at Karabük University in 2018. His research interests include mathematical modeling, optimization, artificial intelligence, wind energy systems, and renewable energy sources.

  • Bahar Demirturk, Izmir Bakırçay University

    Bahar Demirtürk is currently a full Associated Professor at the Department of the Fundamental Sciences in Engineering and Architecture Faculty, and the Intelligent Systems Engineering graduate program in Izmir Bakırçay University, Izmir, Turkey. She obtained her Ph.D. degree in Algebra and Number Theory from Institute of Science in 2010 from Sakarya University. Her research interests include Diophantine equations, combinatorial properties of number sequences, quaternions, logarithmic method, optimization methods, mathematical modeling.

  • Şükran Konca, Izmir Bakırçay University
     

    Şükran Konca is currently a Full Professor at the department of the Fundamental Sciences Department of Izmir Bakırçay University, Izmir, Turkey. She obtained her Ph.D. degree in Topology from Institute of Science in 2014 from Sakarya University. Her research interests include summability theory, sequence spaces and matrix transformations, statistical convergence and ideal convergence, n-normed spaces, n-inner product, 2-inner product in lp spaces, theory of selection principles, optimization methods and modeling.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Optimization

License

Copyright (c) 2025 Bayram Köse, Bahar Demirturk, Şükran Konca

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How to Cite

Application of Search Algorithms to Root-Finding Problems in Algebraic and Transcendental Contexts. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6351. https://doi.org/10.29020/nybg.ejpam.v18i3.6351