Stability Analysis of Jacobian-Free Newton’s Iterative Method
It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial estimations. In multivariate case, multidimensional dynamical analysis allows us...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/12/11/236 |
| _version_ | 1811195126944366592 |
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| author | Abdolreza Amiri Alicia Cordero Mohammad Taghi Darvishi Juan R. Torregrosa |
| author_facet | Abdolreza Amiri Alicia Cordero Mohammad Taghi Darvishi Juan R. Torregrosa |
| author_sort | Abdolreza Amiri |
| collection | DOAJ |
| description | It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial estimations. In multivariate case, multidimensional dynamical analysis allows us to afford this task and it is made on different Jacobian-free variants of Newton’s method, whose estimations of the Jacobian matrix have increasing order. The respective basins of attraction and the number of fixed and critical points give us valuable information in this sense. |
| first_indexed | 2024-04-12T00:38:22Z |
| format | Article |
| id | doaj.art-2e9d22b9e95d4e308c53e4d659976bb2 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-04-12T00:38:22Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-2e9d22b9e95d4e308c53e4d659976bb22022-12-22T03:55:05ZengMDPI AGAlgorithms1999-48932019-11-01121123610.3390/a12110236a12110236Stability Analysis of Jacobian-Free Newton’s Iterative MethodAbdolreza Amiri0Alicia Cordero1Mohammad Taghi Darvishi2Juan R. Torregrosa3Department of Mathematics, Faculty of Science, Razi University, 67149 Kermanshah, IranInstitute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, SpainDepartment of Mathematics, Faculty of Science, Razi University, 67149 Kermanshah, IranInstitute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, SpainIt is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial estimations. In multivariate case, multidimensional dynamical analysis allows us to afford this task and it is made on different Jacobian-free variants of Newton’s method, whose estimations of the Jacobian matrix have increasing order. The respective basins of attraction and the number of fixed and critical points give us valuable information in this sense.https://www.mdpi.com/1999-4893/12/11/236nonlinear system of equationsiterative methodjacobian-free schemebasin of attraction |
| spellingShingle | Abdolreza Amiri Alicia Cordero Mohammad Taghi Darvishi Juan R. Torregrosa Stability Analysis of Jacobian-Free Newton’s Iterative Method Algorithms nonlinear system of equations iterative method jacobian-free scheme basin of attraction |
| title | Stability Analysis of Jacobian-Free Newton’s Iterative Method |
| title_full | Stability Analysis of Jacobian-Free Newton’s Iterative Method |
| title_fullStr | Stability Analysis of Jacobian-Free Newton’s Iterative Method |
| title_full_unstemmed | Stability Analysis of Jacobian-Free Newton’s Iterative Method |
| title_short | Stability Analysis of Jacobian-Free Newton’s Iterative Method |
| title_sort | stability analysis of jacobian free newton s iterative method |
| topic | nonlinear system of equations iterative method jacobian-free scheme basin of attraction |
| url | https://www.mdpi.com/1999-4893/12/11/236 |
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