Closure condition of a function by the Newton-Raphson method
-
2023-11-03 https://doi.org/10.14419/ijbas.v12i1.32399 -
Abstract
The work was developed with the purpose of briefly presenting the Newton-Raphson method for the calculation of real roots of equations. The objective was to present an experiment that would consolidate with the study in simulation format to apply the concepts developed through the root isolation procedures, definition of the initial value by the appropriate interval, as well as in the stopping criteria, by the ge-ometric observation of the tangent line of the graphs and the iteration processes, approximating the values of the reality of the zeros of the function. We also discuss the possible flaws of the simulation system presented, given the rules of the method used.
-
References
- Cardano G (1993), Ars magna or the rules of algebra, Dover, 1545.
- Abel NH (1826), Demonstration de impossibilite de la resolution algebrique des equations generales qui passent le quatrieme degree. J. Reine Angew. Math 1, 65–84.
- Ruggiero MAG & Lopes VLR, Numerical calculus: theoretical and computational aspects, Makron Books. São Paulo (1996).
- Newton I, Fluxions method, Prometeu (1736).
- Raphson J, Analysis aequationum universalis, London (1690).
- Chapra SC & Canale RP, Numerical methods for engineering, Bookman. 5 ed. São Paulo (2011).
- Amaral C, Souza M & Catalan T (2015), A study of the Newton-Raphson method. Revista Eletrônica Matemática e Estatística em Foco 3, 1, 65-72.
- Machado IA & Alves RR (2013), Newton’s method. Revista Eletrônica de Educação da Faculdade Araguaia 4, 4, 30-45.
- Flemming DM & Gonçalves MB, Calculation A: functions, limit, derivation, and integration, Pearson Prentice Hall. 6 ed. São Paulo (2009).
- Campos Filho FF, Numerical algorithms, LTC. 2 ed. Rio de Janeiro (2010).
- Arenales S & Darezzo A, Numerical calculus: software-supported learning, Thompson Learning. 2 ed. São Paulo (2008).
- Guidorizzi HL, A course in calculus, LTC. 5 ed. Rio de Janeiro (2001).
- Sossolete JO, The Newton-Raphson method and applications. Monograph. Faculdade de Ciências Exatas e Tecnologia, Universidade Federal da Grande Dourados, Mato Grosso do Sul (2021).
- Franco NB, Numerical calculation, Pearson Prentice Hall. São Paulo (2006).
- Fritz J, Learning Newton’s method. Wolfram Demonstrations Project (2011). Available: https://demonstrations.wolfram.com/LearningNewtonsMethod/#popup1.
-
Downloads
-
How to Cite
Pereira da Silva , J. (2023). Closure condition of a function by the Newton-Raphson method. International Journal of Basic and Applied Sciences, 12(1), 9-13. https://doi.org/10.14419/ijbas.v12i1.32399