Abstract
Finding the roots of an equation is a fundamental problem in various fields, including numerical computing, social and physical sciences. Numerical techniques are used when an analytic solution is not available. There is not a single algorithm that works best for every function. We designed and implemented a new algorithm that is a dynamic blend of the bisection and regula falsi algorithms. The implementation results validate that the new algorithm outperforms both bisection and regula falsi algorithms. It is also observed that the new algorithm outperforms the secant algorithm and the Newton-Raphson algorithm because the new algorithm requires fewer computational iterations and is guaranteed to find a root. The theoretical and empirical evidence shows that the average computational complexity of the new algorithm is considerably less than that of the classical algorithms.
Recommended Citation
C. Sabharwal, "Blended Root Finding Algorithm Outperforms Bisection and Regula Falsi Algorithms," Mathematics, vol. 7, no. 11, MDPI AG, Nov 2019.
The definitive version is available at https://doi.org/10.3390/math7111118
Department(s)
Computer Science
Keywords and Phrases
Bisection; Blended algorithm; Newton-Raphson; Regula falsi; Secant
International Standard Serial Number (ISSN)
2227-7390
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2019 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Nov 2019
