Note on the efficiency of some iterative methods for solving nonlinear equations
The e ciency of algorithms for solving nonlinear equations is a measure of comparison between di erent iterative methods. In the case of scalar equations two parameters are considered as it is well-known, but frequently in recent literature inaccurate generalizations combining these parameters are u...
| Authors: | ; ; |
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| Format: | Article |
| Publication date: | 2015 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/80875 |
| Online Access: | https://hdl.handle.net/2117/80875 https://dx.doi.org/10.1007/s40324-015-0043-z |
| Access Level: | Open access |
| Keyword: | Mathematical analysis Numerical analysis Nonlinear equations iterative methods divided difference order of convergence efficiency index computational efficiency Anàlisi matemàtica Anàlisi numèrica Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations Classificació AMS::47 Operator theory::47H Nonlinear operators and their properties Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| _version_ | 1878740125157949440 |
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| author | Grau Sánchez, Miguel|||0000-0003-2184-0837 |
| author2 | Noguera Batlle, Miquel|||0000-0003-4629-6874 Díaz Barrero, José Luis |
| author2_role | author author |
| author_browse | Díaz Barrero, José Luis Grau Sánchez, Miguel|||0000-0003-2184-0837 Noguera Batlle, Miquel|||0000-0003-4629-6874 |
| author_facet | Grau Sánchez, Miguel|||0000-0003-2184-0837 Noguera Batlle, Miquel|||0000-0003-4629-6874 Díaz Barrero, José Luis |
| author_role | author |
| collection | UPCommons. Portal del coneixement obert de la UPC |
| description | The e ciency of algorithms for solving nonlinear equations is a measure of comparison between di erent iterative methods. In the case of scalar equations two parameters are considered as it is well-known, but frequently in recent literature inaccurate generalizations combining these parameters are used when solving systems of nonlinear equations. Our goal in this paper is to clarify the concept of the e ciency in the multi-dimensional case. To do it we present a detailed de nition of the computational e ciency. The relation between the e ciency parameters in scalar and vectorial cases is analyzed in detail and tested in two numerical examples |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_cdcda5048490694ffd20cccdebb8c310 |
| institution | Universitat Politècnica de Catalunya (UPC) |
| instname_str | Universitat Politècnica de Catalunya (UPC) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:upcommons.upc.edu:2117/80875 |
| publishDate | 2015 |
| publishDateSort | 2015 |
| reponame_str | UPCommons. Portal del coneixement obert de la UPC |
| spelling | Note on the efficiency of some iterative methods for solving nonlinear equations Grau Sánchez, Miguel|||0000-0003-2184-0837 Noguera Batlle, Miquel|||0000-0003-4629-6874 Díaz Barrero, José Luis Mathematical analysis Numerical analysis Nonlinear equations iterative methods divided difference order of convergence efficiency index computational efficiency Anàlisi matemàtica Anàlisi numèrica Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations Classificació AMS::47 Operator theory::47H Nonlinear operators and their properties Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica The e ciency of algorithms for solving nonlinear equations is a measure of comparison between di erent iterative methods. In the case of scalar equations two parameters are considered as it is well-known, but frequently in recent literature inaccurate generalizations combining these parameters are used when solving systems of nonlinear equations. Our goal in this paper is to clarify the concept of the e ciency in the multi-dimensional case. To do it we present a detailed de nition of the computational e ciency. The relation between the e ciency parameters in scalar and vectorial cases is analyzed in detail and tested in two numerical examples Peer Reviewed https://hdl.handle.net/2117/80875 https://dx.doi.org/10.1007/s40324-015-0043-z |
| spellingShingle | Note on the efficiency of some iterative methods for solving nonlinear equations Grau Sánchez, Miguel|||0000-0003-2184-0837 Mathematical analysis Numerical analysis Nonlinear equations iterative methods divided difference order of convergence efficiency index computational efficiency Anàlisi matemàtica Anàlisi numèrica Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations Classificació AMS::47 Operator theory::47H Nonlinear operators and their properties Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| title | Note on the efficiency of some iterative methods for solving nonlinear equations |
| title_full | Note on the efficiency of some iterative methods for solving nonlinear equations |
| title_fullStr | Note on the efficiency of some iterative methods for solving nonlinear equations |
| title_full_unstemmed | Note on the efficiency of some iterative methods for solving nonlinear equations |
| title_short | Note on the efficiency of some iterative methods for solving nonlinear equations |
| title_sort | Note on the efficiency of some iterative methods for solving nonlinear equations |
| topic | Mathematical analysis Numerical analysis Nonlinear equations iterative methods divided difference order of convergence efficiency index computational efficiency Anàlisi matemàtica Anàlisi numèrica Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations Classificació AMS::47 Operator theory::47H Nonlinear operators and their properties Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| topic_facet | Mathematical analysis Numerical analysis Nonlinear equations iterative methods divided difference order of convergence efficiency index computational efficiency Anàlisi matemàtica Anàlisi numèrica Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations Classificació AMS::47 Operator theory::47H Nonlinear operators and their properties Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| url | https://hdl.handle.net/2117/80875 https://dx.doi.org/10.1007/s40324-015-0043-z |