King-Type Derivative-Free Iterative Families: Real and Memory Dynamics
A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stabilit...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/2713145 |
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| _version_ | 1832548967520403456 |
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| author | F. I. Chicharro A. Cordero J. R. Torregrosa M. P. Vassileva |
| author_facet | F. I. Chicharro A. Cordero J. R. Torregrosa M. P. Vassileva |
| author_sort | F. I. Chicharro |
| collection | DOAJ |
| description | A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties. |
| format | Article |
| id | doaj-art-ac6d6a80ec5d490bb18e2b393806dd08 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ac6d6a80ec5d490bb18e2b393806dd082025-02-03T06:12:37ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/27131452713145King-Type Derivative-Free Iterative Families: Real and Memory DynamicsF. I. Chicharro0A. Cordero1J. R. Torregrosa2M. P. Vassileva3Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, València, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, València, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, València, SpainInstituto Tecnológico de Santo Domingo (INTEC), Santo Domingo, Dominican RepublicA biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.http://dx.doi.org/10.1155/2017/2713145 |
| spellingShingle | F. I. Chicharro A. Cordero J. R. Torregrosa M. P. Vassileva King-Type Derivative-Free Iterative Families: Real and Memory Dynamics Complexity |
| title | King-Type Derivative-Free Iterative Families: Real and Memory Dynamics |
| title_full | King-Type Derivative-Free Iterative Families: Real and Memory Dynamics |
| title_fullStr | King-Type Derivative-Free Iterative Families: Real and Memory Dynamics |
| title_full_unstemmed | King-Type Derivative-Free Iterative Families: Real and Memory Dynamics |
| title_short | King-Type Derivative-Free Iterative Families: Real and Memory Dynamics |
| title_sort | king type derivative free iterative families real and memory dynamics |
| url | http://dx.doi.org/10.1155/2017/2713145 |
| work_keys_str_mv | AT fichicharro kingtypederivativefreeiterativefamiliesrealandmemorydynamics AT acordero kingtypederivativefreeiterativefamiliesrealandmemorydynamics AT jrtorregrosa kingtypederivativefreeiterativefamiliesrealandmemorydynamics AT mpvassileva kingtypederivativefreeiterativefamiliesrealandmemorydynamics |