A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations
A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/836901 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550709511323648 |
|---|---|
| author | Alicia Cordero José L. Hueso Eulalia Martínez Juan R. Torregrosa |
| author_facet | Alicia Cordero José L. Hueso Eulalia Martínez Juan R. Torregrosa |
| author_sort | Alicia Cordero |
| collection | DOAJ |
| description | A family of derivative-free methods of seventh-order
convergence for solving nonlinear equations is suggested. In the proposed
methods, several linear combinations of divided differences are used in
order to get a good estimation of the derivative of the given function at
the different steps of the iteration. The efficiency indices of the members of
this family are equal to 1.6266. Also, numerical examples are used to show
the performance of the presented methods, on smooth and nonsmooth
equations, and to compare with other derivative-free methods, including
some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture. |
| format | Article |
| id | doaj-art-90d72c4b41c3456fa67d3e1f4d5957aa |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-90d72c4b41c3456fa67d3e1f4d5957aa2025-02-03T06:06:01ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/836901836901A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth EquationsAlicia Cordero0José L. Hueso1Eulalia Martínez2Juan R. Torregrosa3Instituto de Matemática Multidisciplinar and Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar and Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar and Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar and Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainA family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.6266. Also, numerical examples are used to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other derivative-free methods, including some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.http://dx.doi.org/10.1155/2012/836901 |
| spellingShingle | Alicia Cordero José L. Hueso Eulalia Martínez Juan R. Torregrosa A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations Abstract and Applied Analysis |
| title | A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations |
| title_full | A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations |
| title_fullStr | A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations |
| title_full_unstemmed | A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations |
| title_short | A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations |
| title_sort | family of derivative free methods with high order of convergence and its application to nonsmooth equations |
| url | http://dx.doi.org/10.1155/2012/836901 |
| work_keys_str_mv | AT aliciacordero afamilyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations AT joselhueso afamilyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations AT eulaliamartinez afamilyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations AT juanrtorregrosa afamilyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations AT aliciacordero familyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations AT joselhueso familyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations AT eulaliamartinez familyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations AT juanrtorregrosa familyofderivativefreemethodswithhighorderofconvergenceanditsapplicationtononsmoothequations |