On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics
With an error corrector via principal branch of the mth root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equa...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/378517 |
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| _version_ | 1832564455525842944 |
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| author | Young Ik Kim Young Hee Geum |
| author_facet | Young Ik Kim Young Hee Geum |
| author_sort | Young Ik Kim |
| collection | DOAJ |
| description | With an error corrector via principal branch of the mth root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented. |
| format | Article |
| id | doaj-art-2641cbb369a2405eb7bbacd28befafa3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2641cbb369a2405eb7bbacd28befafa32025-02-03T01:10:51ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/378517378517On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their DynamicsYoung Ik Kim0Young Hee Geum1Department of Applied Mathematics, Dankook University, Cheonan 330-714, Republic of KoreaDepartment of Applied Mathematics, Dankook University, Cheonan 330-714, Republic of KoreaWith an error corrector via principal branch of the mth root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented.http://dx.doi.org/10.1155/2015/378517 |
| spellingShingle | Young Ik Kim Young Hee Geum On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics Discrete Dynamics in Nature and Society |
| title | On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics |
| title_full | On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics |
| title_fullStr | On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics |
| title_full_unstemmed | On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics |
| title_short | On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics |
| title_sort | on constructing two point optimal fourth order multiple root finders with a generic error corrector and illustrating their dynamics |
| url | http://dx.doi.org/10.1155/2015/378517 |
| work_keys_str_mv | AT youngikkim onconstructingtwopointoptimalfourthordermultiplerootfinderswithagenericerrorcorrectorandillustratingtheirdynamics AT youngheegeum onconstructingtwopointoptimalfourthordermultiplerootfinderswithagenericerrorcorrectorandillustratingtheirdynamics |