{"id":{"repo_id":"dialnet","oai_identifier":"oai:dialnet.unirioja.es:TES0000000216"},"canonical_url":"https://search.dev.ndltd.org/etd/dialnet/oai:dialnet.unirioja.es:TES0000000216","repository":{"repo_id":"dialnet","name":"Dialnet","base_url":"https://dialnet.unirioja.es/oaites/OAIHandler"},"display":{"title":"El método de Newton en espacios de Banach","abstract":"Newton's method is a well known iterative method to solve a nonlinear equation F(x) = 0. We analyze the convergence of this method for operators defined between two Banach spaces, so our results can be applied in a wide range of problems, such as real or complex equations, nonlinear systems of equations, differential or integral equations. Firstly we study Newton's method in terms of the linear operator LFx=F' x-1F ''x F 'x1 Fx. In this sense, new convergence results are given in terms of this operator. Another part of this report is devoted to the study of Newton's method assuming that F satisfies different conditions from the classical ones (Kantorovich). Finally, as an acceleration of Newton's method, a new third order iterative process is obtained. Its basic properties (convergence, unicity of solution, error estimates, etc.) are analysed. This work is mainly theoretical although some results are illustrated with examples.","abstract_html":"Newton's method is a well known iterative method to solve a nonlinear equation F(x) = 0. We analyze the convergence of this method for operators defined between two Banach spaces, so our results can be applied in a wide range of problems, such as real or complex equations, nonlinear systems of equations, differential or integral equations. Firstly we study Newton's method in terms of the linear operator LFx=F' x-1F ''x F 'x1 Fx. In this sense, new convergence results are given in terms of this operator. Another part of this report is devoted to the study of Newton's method assuming that F satisfies different conditions from the classical ones (Kantorovich). Finally, as an acceleration of Newton's method, a new third order iterative process is obtained. Its basic properties (convergence, unicity of solution, error estimates, etc.) are analysed. This work is mainly theoretical although some results are illustrated with examples.","abstract_has_math":false,"creators":["Gutiérrez Jiménez, José Manuel"],"institution":"Universidad de La Rioja (España)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Hernández Verón, Miguel Angel (Universidad de La Rioja)"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1995,"date_issued":"1995","date_published":"1995","updated_at":"2026-07-24T06:26:35Z","subjects":["Ecuaciones no lineares","métodos iterativos","método de Newton","secuencias mayorizantes","Nonlinear equations","iterative methods","Newton's method","majorizing sequences"],"languages":["spa"],"rights":["LICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dialnet.unirioja.es/servlet/oaites?codigo=10","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hernández Verón, Miguel Angel (Universidad de La Rioja)"]},{"key":"dc:creator","label":"Author","values":["Gutiérrez Jiménez, José Manuel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1995"]},{"key":"dc:publisher","label":"Institution","values":["Universidad de La Rioja (España)"]},{"key":"dc:type","label":"Dc Type","values":["text (thesis)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Ecuaciones no lineares","métodos iterativos","método de Newton","secuencias mayorizantes","Nonlinear equations","iterative methods","Newton's method","majorizing sequences"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["spa"]},{"key":"dc:rights","label":"Dc Rights","values":["LICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dialnet.unirioja.es/servlet/oaites?codigo=10"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Newton's method is a well known iterative method to solve a nonlinear equation F(x) = 0. We analyze the convergence of this method for operators defined between two Banach spaces, so our results can be applied in a wide range of problems, such as real or complex equations, nonlinear systems of equations, differential or integral equations. Firstly we study Newton's method in terms of the linear operator LFx=F' x-1F ''x F 'x1 Fx. In this sense, new convergence results are given in terms of this operator. Another part of this report is devoted to the study of Newton's method assuming that F satisfies different conditions from the classical ones (Kantorovich). Finally, as an acceleration of Newton's method, a new third order iterative process is obtained. Its basic properties (convergence, unicity of solution, error estimates, etc.) are analysed. This work is mainly theoretical although some results are illustrated with examples.","El método de Newton es el método iterativo más utilizado para resolver la ecuación no linear F(x) = 0. En esta tesis analizamos la convergencia de este método para operadores definidos entre dos espacios de Banach, por lo que nuestros resultados se pueden aplicar a un amplio rango de problemas, tanto ecuaciones reales como complejas, sistemas de ecuaciones no lineares o ecuaciones diferenciales o integrales. En esta memoria desarrollaremos fundamentalmente la técnica de Kantorovich, en la que, mediante relaciones de recurrencia y el empleo de sucesiones mayorizantes, se establecen condiciones para la convergencia de la sucesión de Newton a una solución de F(x) = 0; además se garantiza la existencia y unicidad de dicha solución en un determinado dominio. El trabajo realizado es mayoritariamente teórico, aunque algunos resultados aparecen ilustrados con ejemplos."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["El método de Newton en espacios de Banach"]}]}],"canonical_facts":{"dc:contributor":["Hernández Verón, Miguel Angel (Universidad de La Rioja)"],"dc:creator":["Gutiérrez Jiménez, José Manuel"],"dc:date":["1995"],"dc:description":["Newton's method is a well known iterative method to solve a nonlinear equation F(x) = 0. We analyze the convergence of this method for operators defined between two Banach spaces, so our results can be applied in a wide range of problems, such as real or complex equations, nonlinear systems of equations, differential or integral equations. Firstly we study Newton's method in terms of the linear operator LFx=F' x-1F ''x F 'x1 Fx. In this sense, new convergence results are given in terms of this operator. Another part of this report is devoted to the study of Newton's method assuming that F satisfies different conditions from the classical ones (Kantorovich). Finally, as an acceleration of Newton's method, a new third order iterative process is obtained. Its basic properties (convergence, unicity of solution, error estimates, etc.) are analysed. This work is mainly theoretical although some results are illustrated with examples.","El método de Newton es el método iterativo más utilizado para resolver la ecuación no linear F(x) = 0. En esta tesis analizamos la convergencia de este método para operadores definidos entre dos espacios de Banach, por lo que nuestros resultados se pueden aplicar a un amplio rango de problemas, tanto ecuaciones reales como complejas, sistemas de ecuaciones no lineares o ecuaciones diferenciales o integrales. En esta memoria desarrollaremos fundamentalmente la técnica de Kantorovich, en la que, mediante relaciones de recurrencia y el empleo de sucesiones mayorizantes, se establecen condiciones para la convergencia de la sucesión de Newton a una solución de F(x) = 0; además se garantiza la existencia y unicidad de dicha solución en un determinado dominio. El trabajo realizado es mayoritariamente teórico, aunque algunos resultados aparecen ilustrados con ejemplos."],"dc:format":["application/pdf"],"dc:identifier":["https://dialnet.unirioja.es/servlet/oaites?codigo=10"],"dc:language":["spa"],"dc:publisher":["Universidad de La Rioja (España)"],"dc:rights":["LICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI"],"dc:subject":["Ecuaciones no lineares","métodos iterativos","método de Newton","secuencias mayorizantes","Nonlinear equations","iterative methods","Newton's method","majorizing sequences"],"dc:title":["El método de Newton en espacios de Banach"],"dc:type":["text (thesis)"]},"updated_at":"2026-07-24T06:26:35Z"}