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
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Argyros, Ioannis K.92e00ca9-9b1e-4b9a-9d4e-154fc7332eeb300George, Santhosh53ecdd2f-64fb-461d-83f7-0c4e1ca0c6533002019-07-03T02:07:22Z2019-07-03T02:07:22Z2017-01-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66435http://bdigital.unal.edu.co/67463/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.Presentamos un análisis de convergencia local para una familia de métodos de tercer orden de tipo Steffensen con el fin de aproximar una solución de una ecuación no lineal. Utilizamos hipótesis hasta la primera derivada en contraste con estudios anteriores como [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] utilizando hipótesis hasta la cuarta derivada. De esta manera, la aplicabilidad de estos métodos se extiende bajo hipótesis más débiles. Además, el radio de convergencia y los límites de error computables en las distancias involucradas también se dan en este estudio. También se presentan ejemplos numéricos en este estudio.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/66831Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasArgyros, Ioannis K. and George, Santhosh (2017) Ball convergence theorem for a Steffensen-type third-order method. Revista Colombiana de Matemáticas, 51 (1). pp. 1-14. ISSN 2357-410051 Matemáticas / MathematicsMétodo de SteffensenMétodo de NewtonOrden de convergenciaConvergencia localSteffensen's methodNewton's methodorder of convergencelocal convergenceBall convergence theorem for a Steffensen-type third-order methodArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL66831-342832-1-SM.pdfapplication/pdf348376https://repositorio.unal.edu.co/bitstream/unal/66435/1/66831-342832-1-SM.pdf72e200400f5fbe1b73c735c24eea9e8fMD51THUMBNAIL66831-342832-1-SM.pdf.jpg66831-342832-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg4970https://repositorio.unal.edu.co/bitstream/unal/66435/2/66831-342832-1-SM.pdf.jpg5f1965ae5e1b63142f6fa0a92aabd65fMD52unal/66435oai:repositorio.unal.edu.co:unal/664352024-05-16 23:09:24.041Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
Ball convergence theorem for a Steffensen-type third-order method |
| title |
Ball convergence theorem for a Steffensen-type third-order method |
| spellingShingle |
Ball convergence theorem for a Steffensen-type third-order method 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 |
| title_short |
Ball convergence theorem for a Steffensen-type third-order method |
| title_full |
Ball convergence theorem for a Steffensen-type third-order method |
| title_fullStr |
Ball convergence theorem for a Steffensen-type third-order method |
| title_full_unstemmed |
Ball convergence theorem for a Steffensen-type third-order method |
| title_sort |
Ball convergence theorem for a Steffensen-type third-order method |
| dc.creator.fl_str_mv |
Argyros, Ioannis K. George, Santhosh |
| dc.contributor.author.spa.fl_str_mv |
Argyros, Ioannis K. George, Santhosh |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics |
| topic |
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 |
| dc.subject.proposal.spa.fl_str_mv |
Método de Steffensen Método de Newton Orden de convergencia Convergencia local Steffensen's method Newton's method order of convergence local convergence |
| description |
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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2017 |
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2017-01-01 |
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2019-07-03T02:07:22Z |
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2019-07-03T02:07:22Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Text |
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http://purl.org/redcol/resource_type/ART |
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publishedVersion |
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ISSN: 2357-4100 |
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https://repositorio.unal.edu.co/handle/unal/66435 |
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http://bdigital.unal.edu.co/67463/ |
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ISSN: 2357-4100 |
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spa |
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spa |
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https://revistas.unal.edu.co/index.php/recolma/article/view/66831 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
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Argyros, Ioannis K. and George, Santhosh (2017) Ball convergence theorem for a Steffensen-type third-order method. Revista Colombiana de Matemáticas, 51 (1). pp. 1-14. ISSN 2357-4100 |
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Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
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