Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure
We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the v...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/289029 |
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| author | Santiago Artidiello Alicia Cordero Juan R. Torregrosa María P. Vassileva |
| author_facet | Santiago Artidiello Alicia Cordero Juan R. Torregrosa María P. Vassileva |
| author_sort | Santiago Artidiello |
| collection | DOAJ |
| description | We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points. |
| format | Article |
| id | doaj-art-2ad360978f6e476fb7996e8ab6c56762 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2ad360978f6e476fb7996e8ab6c567622025-02-03T01:25:29ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/289029289029Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function ProcedureSantiago Artidiello0Alicia Cordero1Juan R. Torregrosa2María P. Vassileva3Instituto Tecnológico de Santo Domingo (INTEC), Avenida Los Próceres, Galá, 10602 Santo Domingo, Dominican RepublicInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, SpainInstituto Tecnológico de Santo Domingo (INTEC), Avenida Los Próceres, Galá, 10602 Santo Domingo, Dominican RepublicWe present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.http://dx.doi.org/10.1155/2015/289029 |
| spellingShingle | Santiago Artidiello Alicia Cordero Juan R. Torregrosa María P. Vassileva Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure Abstract and Applied Analysis |
| title | Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure |
| title_full | Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure |
| title_fullStr | Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure |
| title_full_unstemmed | Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure |
| title_short | Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure |
| title_sort | design of high order iterative methods for nonlinear systems by using weight function procedure |
| url | http://dx.doi.org/10.1155/2015/289029 |
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