Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions
In the present paper, we consider a construction proposed in Xiao and Yin (2016) to improve the order of convergence of the method from p to p + 2m under weaker assumptions. Using the idea of restricted convergence domains we extend the applicability of the method considered by Xiao and Yin (2016)....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2019-06-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/awutm-2019-0006 |
| _version_ | 1818191907918970880 |
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| author | Argyros Ioannis K. George Santhosh Erappa Shobha M. |
| author_facet | Argyros Ioannis K. George Santhosh Erappa Shobha M. |
| author_sort | Argyros Ioannis K. |
| collection | DOAJ |
| description | In the present paper, we consider a construction proposed in Xiao and Yin (2016) to improve the order of convergence of the method from p to p + 2m under weaker assumptions. Using the idea of restricted convergence domains we extend the applicability of the method considered by Xiao and Yin (2016). Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. |
| first_indexed | 2024-12-12T00:22:04Z |
| format | Article |
| id | doaj.art-ba048df90d03445f9ee8ca2f4b13f159 |
| institution | Directory Open Access Journal |
| issn | 1841-3307 |
| language | English |
| last_indexed | 2024-12-12T00:22:04Z |
| publishDate | 2019-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annals of the West University of Timisoara: Mathematics and Computer Science |
| spelling | doaj.art-ba048df90d03445f9ee8ca2f4b13f1592022-12-22T00:44:42ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072019-06-01571536510.2478/awutm-2019-0006awutm-2019-0006Increasing the order of convergence of multistep methods for solving systems of equations under weak conditionsArgyros Ioannis K.0George Santhosh1Erappa Shobha M.2Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematical and Computational Sciences,NITKarnataka, India-575 025Department of Mathematics, Manipal Institute of Technology, Manipal, Karnataka, India-576104In the present paper, we consider a construction proposed in Xiao and Yin (2016) to improve the order of convergence of the method from p to p + 2m under weaker assumptions. Using the idea of restricted convergence domains we extend the applicability of the method considered by Xiao and Yin (2016). Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.https://doi.org/10.2478/awutm-2019-0006newton’s methodradius of convergencelocal convergence |
| spellingShingle | Argyros Ioannis K. George Santhosh Erappa Shobha M. Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions Annals of the West University of Timisoara: Mathematics and Computer Science newton’s method radius of convergence local convergence |
| title | Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions |
| title_full | Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions |
| title_fullStr | Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions |
| title_full_unstemmed | Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions |
| title_short | Increasing the order of convergence of multistep methods for solving systems of equations under weak conditions |
| title_sort | increasing the order of convergence of multistep methods for solving systems of equations under weak conditions |
| topic | newton’s method radius of convergence local convergence |
| url | https://doi.org/10.2478/awutm-2019-0006 |
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