Conceptualizing the Iterative method of Newton-Raphson for systems with two equations
DOI:
https://doi.org/10.56294/sctconf2023525Keywords:
Mathematics, Computer Science, AlgorithmsAbstract
In numerical analysis, Newton-Raphson method is a root-finding algorithm which generates iterative approximations to the zeroes (or roots) of a real-valued function. This paper describes in a detailed way the mathematical background around the iterative method of Newton-Raphson for systems with two equations. Next, an algorithmic implementation of the iterative method of Newton-Raphson for systems with two equations is developed in Pascal Programming Language, to represent the steps of this method with a procedural programming language with special emphasis on the use of computing in the scientific area of mathematics.
References
1. J.M. McNamee: "Numerical Methods for Roots of Polynomials - Part I", Elsevier (2007).
2. J.M. McNamee and Victor Pan: "Numerical Methods for Roots of Polynomials - Part II", Elsevier (2013).
3. Triantafyllou, S. A. (2022). Constructivist Learning Environments. Proceedings of The 5th International Conference on Advanced Research in Teaching and Education, 2022. https://www.doi.org/10.33422/5th.icate.2022.04.10
4. Triantafyllou, S.A. (2023). A Quantitative Research About MOOCs and EdTech Tools for Distance Learning. In: Auer, M.E., El-Seoud, S.A., Karam, O.H. (eds) Artificial Intelligence and Online Engineering. REV 2022. Lecture Notes in Networks and Systems, vol 524. Springer, Cham. https://doi.org/10.1007/978-3-031-17091-1_52
5. Triantafyllou, S.A. (2022). TPACK and Toondoo Digital Storytelling Tool Transform Teaching and Learning. In: Florez, H., Gomez, H. (eds) Applied Informatics. ICAI 2022. Communications in Computer and Information Science, vol 1643. Springer, Cham. https://doi.org/10.1007/978-3-031-19647-8_24
6. Farhaoui, Y.and All, Big Data Mining and Analytics, 2023, 6(3), pp. I–II, DOI: 10.26599/BDMA.2022.9020045
7. Triantafyllou, S. A., & Sapounidis, T. (2023). Game-based Learning approach and Serious Games to learn while you play. 2023 IEEE World Engineering Education Conference (EDUNINE). https://doi.org/10.1109/EDUNINE57531.2023.10102872
8. Triantafyllou, S. A., & Georgiadis, C. K. (2022). Gamification Design Patterns for user engagement. Informatics in Education, 655–674. https://doi.org/10.15388/infedu.2022.27
9. Triantafyllou, S.A. (2023). A Detailed Study on the 8 Queens Problem Based on Algorithmic Approaches Implemented in PASCAL Programming Language. In: Silhavy, R., Silhavy, P. (eds) Software Engineering Research in System Science. CSOC 2023. Lecture Notes in Networks and Systems, vol 722. Springer, Cham. https://doi.org/10.1007/978-3-031-35311-6_18
10. Triantafyllou, S. A. (2022). Magic squares in order 4K+2. 2022 30th National Conference with International Participation (TELECOM). https://doi.org/10.1109/TELECOM56127.2022.10017312
11. Triantafyllou, S. A. (2023). Aristotle’s Rhetoric and Semiotics. iNTERCULTURAL tRANSLATION iNTERSEMIOTIC, 12(2). https://doi.org/10.26262/iti.v12i2.9874
12. Triantafyllou, S. Gamification and new approaches in Engineering Education. Preprints 2023, 2023120198. https://doi.org/10.20944/preprints202312.0198.v1
13. Ben-Israel, A. (1966). A Newton-Raphson method for the solution of systems of equations. Journal of Mathematical analysis and applications, 15(2), 243-252.
14. Farhaoui, Y. and All, Big Data Mining and Analytics, 2022, 5(4), pp. I IIDOI: 10.26599/BDMA.2022.9020004
15. Bruck, H. A., McNeill, S. R., Sutton, M. A., & Peters, W. H. (1989). Digital image correlation using Newton-Raphson method of partial differential correction. Experimental mechanics, 29, 261-267.
16. Hartmann, S. (2005). A remark on the application of the Newton-Raphson method in non-linear finite element analysis. Computational Mechanics, 36, 100-116.
17. Pho, K. H. (2022). Improvements of the Newton–Raphson method. Journal of Computational and Applied Mathematics, 408, 114106.
18. Triantafyllou, S.A.: The Effects of Constructivism Theory in the Environment of E-learning. GRIN Verlag, Munich (2013)
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Serafeim A. Triantafyllou (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
The article is distributed under the Creative Commons Attribution 4.0 License. Unless otherwise stated, associated published material is distributed under the same licence.
