Abstract
Finding the roots of non-linear and transcendental equations is an important problem in engineering sciences. In general, such problems do not have an analytic solution; the researchers resort to numerical techniques for exploring. We design and implement a three-way hybrid algorithm that is a blend of the Newton–Raphson algorithm and a two-way blended algorithm (blend of two methods, Bisection and False Position). The hybrid algorithm is a new single pass iterative approach. The method takes advantage of the best in three algorithms in each iteration to estimate an approximate value closer to the root. We show that the new algorithm outperforms the Bisection, Regula Falsi, Newton–Raphson, quadrature based, undetermined coefficients based, and decomposition-based algorithms. The new hybrid root finding algorithm is guaranteed to converge. The experimental results and empirical evidence show that the complexity of the hybrid algorithm is far less than that of other algorithms. Several functions cited in the literature are used as benchmarks to compare and confirm the simplicity, efficiency, and performance of the proposed method.
Recommended Citation
C. L. Sabharwal, "An Iterative Hybrid Algorithm for Roots of Non-Linear Equations," Eng, vol. 2, no. 1, pp. 80 - 98, MDPI, Mar 2021.
The definitive version is available at https://doi.org/10.3390/eng2010007
Department(s)
Computer Science
Publication Status
Open Access
Keywords and Phrases
bisection; false position; newton; order of convergence; predictor-corrector; quadrature
International Standard Serial Number (ISSN)
2673-4117
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2024 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Mar 2021
