Dynamics and Fractal Dimension of Steffensen-Type Methods
In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2015-06-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1999-4893/8/2/271 |
| _version_ | 1811237514217783296 |
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| author | Francisco I. Chicharro Alicia Cordero Juan R. Torregrosa |
| author_facet | Francisco I. Chicharro Alicia Cordero Juan R. Torregrosa |
| author_sort | Francisco I. Chicharro |
| collection | DOAJ |
| description | In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based on the box-counting algorithm, several iterative derivative-free methods of different convergence orders are compared. |
| first_indexed | 2024-04-12T12:24:49Z |
| format | Article |
| id | doaj.art-c47de4bc61754d98ab686c299a335fca |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-04-12T12:24:49Z |
| publishDate | 2015-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-c47de4bc61754d98ab686c299a335fca2022-12-22T03:33:12ZengMDPI AGAlgorithms1999-48932015-06-018227127910.3390/a8020271a8020271Dynamics and Fractal Dimension of Steffensen-Type MethodsFrancisco I. Chicharro0Alicia Cordero1Juan R. Torregrosa2Institute of Telecommunications and Multimedia Applications (iTEAM), Universitat Politècnica de Valencia, Camino de Vera, s/n, 46022-Valencia, SpainInstitute of Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera, s/n,46022-Valencia, SpainInstitute of Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera, s/n,46022-Valencia, SpainIn this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based on the box-counting algorithm, several iterative derivative-free methods of different convergence orders are compared.http://www.mdpi.com/1999-4893/8/2/271nonlinear equationderivative-freedynamical planefractal dimensionPadé-like approximant |
| spellingShingle | Francisco I. Chicharro Alicia Cordero Juan R. Torregrosa Dynamics and Fractal Dimension of Steffensen-Type Methods Algorithms nonlinear equation derivative-free dynamical plane fractal dimension Padé-like approximant |
| title | Dynamics and Fractal Dimension of Steffensen-Type Methods |
| title_full | Dynamics and Fractal Dimension of Steffensen-Type Methods |
| title_fullStr | Dynamics and Fractal Dimension of Steffensen-Type Methods |
| title_full_unstemmed | Dynamics and Fractal Dimension of Steffensen-Type Methods |
| title_short | Dynamics and Fractal Dimension of Steffensen-Type Methods |
| title_sort | dynamics and fractal dimension of steffensen type methods |
| topic | nonlinear equation derivative-free dynamical plane fractal dimension Padé-like approximant |
| url | http://www.mdpi.com/1999-4893/8/2/271 |
| work_keys_str_mv | AT franciscoichicharro dynamicsandfractaldimensionofsteffensentypemethods AT aliciacordero dynamicsandfractaldimensionofsteffensentypemethods AT juanrtorregrosa dynamicsandfractaldimensionofsteffensentypemethods |