Ball convergence theorem for a Steffensen-type third-order method
We present a local convergence analysis for a family of Steffensen-type third-order methods in order to approximate a solution of a nonlinear equation. We use hypothesis up to the first derivative in contrast to earlier studies such as [2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 19, 20, 2...
- Autores:
-
Argyros, Ioannis K.
George, Santhosh
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2017
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66435
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66435
http://bdigital.unal.edu.co/67463/
- Palabra clave:
- 51 Matemáticas / Mathematics
Método de Steffensen
Método de Newton
Orden de convergencia
Convergencia local
Steffensen's method
Newton's method
order of convergence
local convergence
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | We present a local convergence analysis for a family of Steffensen-type third-order methods in order to approximate a solution of a nonlinear equation. We use hypothesis up to the first derivative in contrast to earlier studies such as [2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28] using hypotheses up to the fourth derivative. This way the applicability of these methods is extended under weaker hypothesis. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study. |
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