Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder
The asymptotic form of the Taylor-Lagrange remainder is used to derive some new, efficient, high-order methods to iteratively locate the root, simple or multiple, of a nonlinear function. Also derived are superquadratic methods that converge contrarily and superlinear and supercubic methods that con...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/108976 |
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| _version_ | 1832558830666383360 |
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| author | Isaac Fried |
| author_facet | Isaac Fried |
| author_sort | Isaac Fried |
| collection | DOAJ |
| description | The asymptotic form of the Taylor-Lagrange remainder is used to derive some new, efficient, high-order methods to iteratively locate the root, simple or multiple, of a nonlinear function. Also derived are superquadratic methods that converge contrarily and superlinear and supercubic methods that converge alternatingly, enabling us not only to approach, but also to bracket the root. |
| format | Article |
| id | doaj-art-d964f8e115724f58803328a615038c96 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d964f8e115724f58803328a615038c962025-02-03T01:31:28ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/108976108976Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange RemainderIsaac Fried0Department of Mathematics, Boston University, Boston, MA 02215, USAThe asymptotic form of the Taylor-Lagrange remainder is used to derive some new, efficient, high-order methods to iteratively locate the root, simple or multiple, of a nonlinear function. Also derived are superquadratic methods that converge contrarily and superlinear and supercubic methods that converge alternatingly, enabling us not only to approach, but also to bracket the root.http://dx.doi.org/10.1155/2014/108976 |
| spellingShingle | Isaac Fried Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder Journal of Applied Mathematics |
| title | Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder |
| title_full | Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder |
| title_fullStr | Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder |
| title_full_unstemmed | Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder |
| title_short | Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder |
| title_sort | effective high order iterative methods via the asymptotic form of the taylor lagrange remainder |
| url | http://dx.doi.org/10.1155/2014/108976 |
| work_keys_str_mv | AT isaacfried effectivehighorderiterativemethodsviatheasymptoticformofthetaylorlagrangeremainder |