A study of optimization for Steffensen-type methods with frozen divided differences
| Autor: | Miquel Noguera, Miguel Ángel Hernández-Verón, Miquel Grau-Sánchez, José Antonio Ezquerro |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| Rok vydání: | 2015 |
| Předmět: |
Anàlisi numèrica
Numerical Analysis Control and Optimization Iterative method Generalization Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics [Àrees temàtiques de la UPC] Applied Mathematics 65 Numerical analysis::65H Nonlinear algebraic or transcendental equations [Classificació AMS] Mathematical analysis Type (model theory) system of nonlinear equations Numerical methods and algorithms Divided difference iterative methods Local convergence order of convergence Nonlinear system Rate of convergence efficiency Modeling and Simulation Convergence (routing) Applied mathematics Divided differences Mathematics |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| ISSN: | 2281-7875 2254-3902 |
| Popis: | A local convergence analysis for a generalization of a family of Ste ensen-type iterative methods with three frozen steps is presented for solving nonlinear equations. From the use of three classical divided di erence operators, we study four families of iterative methods with optimal local order of convergence. Then, new variants of the family of iterative methods is constructed, where a study of the computational e ciency is carried out. Moreover, the semilocal convergence for these families is also studied. Finally, an application of nonlinear integral equations of mixed Hammerstein type is presented, where multiple precision and a stopping criterion are implemented without using any known root. In addition, a study, where we compare orders, e ciencies and elapsed times of the methods suggested, supports the theoretical results obtained. |
| Databáze: | OpenAIRE |
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