Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants
We present new high-order optimal iterative methods for solving a nonlinear equation, f(x)=0, by using Padé-like approximants. We compose optimal methods of order 4 with Newton’s step and substitute the derivative by using an appropriate rational approximant, getting optimal methods of order 8. In t...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/3204652 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565754996719616 |
|---|---|
| author | Alicia Cordero José L. Hueso Eulalia Martínez Juan R. Torregrosa |
| author_facet | Alicia Cordero José L. Hueso Eulalia Martínez Juan R. Torregrosa |
| author_sort | Alicia Cordero |
| collection | DOAJ |
| description | We present new high-order optimal iterative methods for solving a nonlinear equation, f(x)=0, by using Padé-like approximants. We compose optimal methods of order 4 with Newton’s step and substitute the derivative by using an appropriate rational approximant, getting optimal methods of order 8. In the same way, increasing the degree of the approximant, we obtain optimal methods of order 16. We also perform different numerical tests that confirm the theoretical results. |
| format | Article |
| id | doaj-art-ec9efdb0771649ba9bae2969524df6f0 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ec9efdb0771649ba9bae2969524df6f02025-02-03T01:06:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/32046523204652Multistep High-Order Methods for Nonlinear Equations Using Padé-Like ApproximantsAlicia Cordero0José L. Hueso1Eulalia Martínez2Juan R. Torregrosa3Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainWe present new high-order optimal iterative methods for solving a nonlinear equation, f(x)=0, by using Padé-like approximants. We compose optimal methods of order 4 with Newton’s step and substitute the derivative by using an appropriate rational approximant, getting optimal methods of order 8. In the same way, increasing the degree of the approximant, we obtain optimal methods of order 16. We also perform different numerical tests that confirm the theoretical results.http://dx.doi.org/10.1155/2017/3204652 |
| spellingShingle | Alicia Cordero José L. Hueso Eulalia Martínez Juan R. Torregrosa Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants Discrete Dynamics in Nature and Society |
| title | Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants |
| title_full | Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants |
| title_fullStr | Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants |
| title_full_unstemmed | Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants |
| title_short | Multistep High-Order Methods for Nonlinear Equations Using Padé-Like Approximants |
| title_sort | multistep high order methods for nonlinear equations using pade like approximants |
| url | http://dx.doi.org/10.1155/2017/3204652 |
| work_keys_str_mv | AT aliciacordero multistephighordermethodsfornonlinearequationsusingpadelikeapproximants AT joselhueso multistephighordermethodsfornonlinearequationsusingpadelikeapproximants AT eulaliamartinez multistephighordermethodsfornonlinearequationsusingpadelikeapproximants AT juanrtorregrosa multistephighordermethodsfornonlinearequationsusingpadelikeapproximants |