Study of a Biparametric Family of Iterative Methods
The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c-iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree po...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/141643 |
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| _version_ | 1832552133736529920 |
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| author | B. Campos A. Cordero Á. A. Magreñán J. R. Torregrosa P. Vindel |
| author_facet | B. Campos A. Cordero Á. A. Magreñán J. R. Torregrosa P. Vindel |
| author_sort | B. Campos |
| collection | DOAJ |
| description | The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c-iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of (α, c) with clear stable and unstable behaviors. |
| format | Article |
| id | doaj-art-0bd7d4f7686443b29b2d7bb354e41db8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0bd7d4f7686443b29b2d7bb354e41db82025-02-03T05:59:25ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/141643141643Study of a Biparametric Family of Iterative MethodsB. Campos0A. Cordero1Á. A. Magreñán2J. R. Torregrosa3P. Vindel4Instituto de Matemáticas y Aplicaciones de Castellón, Universitat Jaume I, 12071 Castellón, SpainInstituto de Matemática Multidisciplinar, Universitat Politécnica de Valencia, 46022 Valencia, SpainUniversidad Internacional de la Rioja, 26002 Logroño, SpainInstituto de Matemática Multidisciplinar, Universitat Politécnica de Valencia, 46022 Valencia, SpainInstituto de Matemáticas y Aplicaciones de Castellón, Universitat Jaume I, 12071 Castellón, SpainThe dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c-iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of (α, c) with clear stable and unstable behaviors.http://dx.doi.org/10.1155/2014/141643 |
| spellingShingle | B. Campos A. Cordero Á. A. Magreñán J. R. Torregrosa P. Vindel Study of a Biparametric Family of Iterative Methods Abstract and Applied Analysis |
| title | Study of a Biparametric Family of Iterative Methods |
| title_full | Study of a Biparametric Family of Iterative Methods |
| title_fullStr | Study of a Biparametric Family of Iterative Methods |
| title_full_unstemmed | Study of a Biparametric Family of Iterative Methods |
| title_short | Study of a Biparametric Family of Iterative Methods |
| title_sort | study of a biparametric family of iterative methods |
| url | http://dx.doi.org/10.1155/2014/141643 |
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