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 |
| Summary: | 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 |
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