Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications
Comparisons between Newton’s and Steffensen-like methods are given for solving systems of equations as well as Banach space valued equations. Our idea of the restricted convergence domain is used to compare the sufficient convergence criteria of these methods under the same conditions as in previous...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2851 |
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| author | Ioannis K. Argyros Christopher Argyros Johan Ceballos Daniel González |
| author_facet | Ioannis K. Argyros Christopher Argyros Johan Ceballos Daniel González |
| author_sort | Ioannis K. Argyros |
| collection | DOAJ |
| description | Comparisons between Newton’s and Steffensen-like methods are given for solving systems of equations as well as Banach space valued equations. Our idea of the restricted convergence domain is used to compare the sufficient convergence criteria of these methods under the same conditions as in previous papers. It turns out that the following advantages are shown: enlarged convergence domain; tighter error estimates and a more precise information on the location of the solution. Advantages are obtained under the same or at least as tight Lipschitz constants, which are specializations of earlier ones. Hence, the applicability of these methods is extended. Numerical experiments complete this study. |
| first_indexed | 2024-03-09T13:01:22Z |
| format | Article |
| id | doaj.art-fcf8919b0eb44f0db1203f5d64c9a666 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:01:22Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fcf8919b0eb44f0db1203f5d64c9a6662023-11-30T21:54:26ZengMDPI AGMathematics2227-73902022-08-011016285110.3390/math10162851Extended Comparative Study between Newton’s and Steffensen-like Methods with ApplicationsIoannis K. Argyros0Christopher Argyros1Johan Ceballos2Daniel González3Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Computing and Technology, Cameron University, Lawton, OK 73505, USAFacultad de Ingeniería y Ciencias Aplicadas, Universidad de Las Américas, Quito 170124, EcuadorFacultad de Ingeniería y Ciencias Aplicadas, Universidad de Las Américas, Quito 170124, EcuadorComparisons between Newton’s and Steffensen-like methods are given for solving systems of equations as well as Banach space valued equations. Our idea of the restricted convergence domain is used to compare the sufficient convergence criteria of these methods under the same conditions as in previous papers. It turns out that the following advantages are shown: enlarged convergence domain; tighter error estimates and a more precise information on the location of the solution. Advantages are obtained under the same or at least as tight Lipschitz constants, which are specializations of earlier ones. Hence, the applicability of these methods is extended. Numerical experiments complete this study.https://www.mdpi.com/2227-7390/10/16/2851semi-local convergenceBanach spaceSteffensen-like methodNewton’s method |
| spellingShingle | Ioannis K. Argyros Christopher Argyros Johan Ceballos Daniel González Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications Mathematics semi-local convergence Banach space Steffensen-like method Newton’s method |
| title | Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications |
| title_full | Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications |
| title_fullStr | Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications |
| title_full_unstemmed | Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications |
| title_short | Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications |
| title_sort | extended comparative study between newton s and steffensen like methods with applications |
| topic | semi-local convergence Banach space Steffensen-like method Newton’s method |
| url | https://www.mdpi.com/2227-7390/10/16/2851 |
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