Two derivative-free methods for solving underdetermined nonlinear systems of equations
- Autores
- Echebest, Nélida Ester; Schuverdt, María Laura; Vignau, Raúl Pedro
- Año de publicación
- 2011
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.
Facultad de Ciencias Exactas - Materia
-
Ciencias Exactas
Matemática
derivative-free line search
global convergence
quasi-Newton method
spectral step length
underdetermined nonlinear systems - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc/3.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/40172
Ver los metadatos del registro completo
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Two derivative-free methods for solving underdetermined nonlinear systems of equationsEchebest, Nélida EsterSchuverdt, María LauraVignau, Raúl PedroCiencias ExactasMatemáticaderivative-free line searchglobal convergencequasi-Newton methodspectral step lengthunderdetermined nonlinear systemsIn this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.Facultad de Ciencias Exactas2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf217-245http://sedici.unlp.edu.ar/handle/10915/40172enginfo:eu-repo/semantics/altIdentifier/url/http://www.scielo.br/pdf/cam/v30n1/11.pdfinfo:eu-repo/semantics/altIdentifier/issn/0101-8205info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/3.0/Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T16:38:40Zoai:sedici.unlp.edu.ar:10915/40172Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 16:38:40.905SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Two derivative-free methods for solving underdetermined nonlinear systems of equations |
| title |
Two derivative-free methods for solving underdetermined nonlinear systems of equations |
| spellingShingle |
Two derivative-free methods for solving underdetermined nonlinear systems of equations Echebest, Nélida Ester Ciencias Exactas Matemática derivative-free line search global convergence quasi-Newton method spectral step length underdetermined nonlinear systems |
| title_short |
Two derivative-free methods for solving underdetermined nonlinear systems of equations |
| title_full |
Two derivative-free methods for solving underdetermined nonlinear systems of equations |
| title_fullStr |
Two derivative-free methods for solving underdetermined nonlinear systems of equations |
| title_full_unstemmed |
Two derivative-free methods for solving underdetermined nonlinear systems of equations |
| title_sort |
Two derivative-free methods for solving underdetermined nonlinear systems of equations |
| dc.creator.none.fl_str_mv |
Echebest, Nélida Ester Schuverdt, María Laura Vignau, Raúl Pedro |
| author |
Echebest, Nélida Ester |
| author_facet |
Echebest, Nélida Ester Schuverdt, María Laura Vignau, Raúl Pedro |
| author_role |
author |
| author2 |
Schuverdt, María Laura Vignau, Raúl Pedro |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Matemática derivative-free line search global convergence quasi-Newton method spectral step length underdetermined nonlinear systems |
| topic |
Ciencias Exactas Matemática derivative-free line search global convergence quasi-Newton method spectral step length underdetermined nonlinear systems |
| dc.description.none.fl_txt_mv |
In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented. Facultad de Ciencias Exactas |
| description |
In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martínez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented. |
| publishDate |
2011 |
| dc.date.none.fl_str_mv |
2011 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://sedici.unlp.edu.ar/handle/10915/40172 |
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| dc.language.none.fl_str_mv |
eng |
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eng |
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info:eu-repo/semantics/altIdentifier/url/http://www.scielo.br/pdf/cam/v30n1/11.pdf info:eu-repo/semantics/altIdentifier/issn/0101-8205 |
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openAccess |
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http://creativecommons.org/licenses/by-nc/3.0/ Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0) |
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