Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations
In the earlier work, expensive Taylor formula and conditions on derivatives up to the eighth order have been utilized to establish the convergence of a derivative free class of seventh order iterative algorithms. Moreover, no error distances or results on uniqueness of the solution were given. In th...
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| Format: | Article |
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Ivan Franko National University of Lviv
2021-10-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/228 |
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| author | I.K. Argyros D. Sharma C.I. Argyros S.K. Parhi S.K. Sunanda M.I. Argyros |
| author_facet | I.K. Argyros D. Sharma C.I. Argyros S.K. Parhi S.K. Sunanda M.I. Argyros |
| author_sort | I.K. Argyros |
| collection | DOAJ |
| description | In the earlier work, expensive Taylor formula and conditions on derivatives up to the eighth
order have been utilized to establish the convergence of a derivative free class of seventh order
iterative algorithms. Moreover, no error distances or results on uniqueness of the solution were
given. In this study, extended ball convergence analysis is derived for this class by imposing
conditions on the first derivative. Additionally, we offer error distances and convergence radius
together with the region of uniqueness for the solution. Therefore, we enlarge the practical
utility of these algorithms. Also, convergence regions of a specific member of this class are displayed
for solving complex polynomial equations. At the end, standard numerical applications
are provided to illustrate the efficacy of our theoretical findings. |
| format | Article |
| id | doaj-art-7346ef564cbc4488ab0967c844c96f19 |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2021-10-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-7346ef564cbc4488ab0967c844c96f192025-08-20T03:33:31ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202021-10-01561728210.30970/ms.56.1.72-82228Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equationsI.K. Argyros0D. Sharma1C.I. Argyros2S.K. Parhi3S.K. Sunanda4M.I. Argyros5Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematics, IIIT Bhubaneswar, Odisha, IndiaDepartment of Computer Science, University of Oklahoma, Norman, OK 73071, USADepartment of Mathematics, Fakir Mohan University, Odisha 756020, IndiaDepartment of Mathematics, IIIT Bhubaneswar, Odisha 751003, IndiaDepartment of Computer Science, Cameron University, Lawton, OK 73505, USAIn the earlier work, expensive Taylor formula and conditions on derivatives up to the eighth order have been utilized to establish the convergence of a derivative free class of seventh order iterative algorithms. Moreover, no error distances or results on uniqueness of the solution were given. In this study, extended ball convergence analysis is derived for this class by imposing conditions on the first derivative. Additionally, we offer error distances and convergence radius together with the region of uniqueness for the solution. Therefore, we enlarge the practical utility of these algorithms. Also, convergence regions of a specific member of this class are displayed for solving complex polynomial equations. At the end, standard numerical applications are provided to illustrate the efficacy of our theoretical findings.http://matstud.org.ua/ojs/index.php/matstud/article/view/228derivative free iterative algorithm;order of convergence;banach space;ball convergence |
| spellingShingle | I.K. Argyros D. Sharma C.I. Argyros S.K. Parhi S.K. Sunanda M.I. Argyros Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations Математичні Студії derivative free iterative algorithm; order of convergence; banach space; ball convergence |
| title | Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations |
| title_full | Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations |
| title_fullStr | Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations |
| title_full_unstemmed | Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations |
| title_short | Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations |
| title_sort | extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations |
| topic | derivative free iterative algorithm; order of convergence; banach space; ball convergence |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/228 |
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