Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations
Steffensen-type methods with memory were originally designed to solve nonlinear equations without the use of additional functional evaluations per computing step. In this paper, a variant of Steffensen’s method is proposed which is derivative-free and with memory. In fact, using an acceler...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/3/306 |
| _version_ | 1811269263398273024 |
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| author | Fuad W. Khdhr Rostam K. Saeed Fazlollah Soleymani |
| author_facet | Fuad W. Khdhr Rostam K. Saeed Fazlollah Soleymani |
| author_sort | Fuad W. Khdhr |
| collection | DOAJ |
| description | Steffensen-type methods with memory were originally designed to solve nonlinear equations without the use of additional functional evaluations per computing step. In this paper, a variant of Steffensen’s method is proposed which is derivative-free and with memory. In fact, using an acceleration technique via interpolation polynomials of appropriate degrees, the computational efficiency index of this scheme is improved. It is discussed that the new scheme is quite fast and has a high efficiency index. Finally, numerical investigations are brought forward to uphold the theoretical discussions. |
| first_indexed | 2024-04-12T21:38:58Z |
| format | Article |
| id | doaj.art-87ababd87eae497cb381abc732917bc3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-12T21:38:58Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-87ababd87eae497cb381abc732917bc32022-12-22T03:15:49ZengMDPI AGMathematics2227-73902019-03-017330610.3390/math7030306math7030306Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear EquationsFuad W. Khdhr0Rostam K. Saeed1Fazlollah Soleymani2Department of Mathematics, College of Science, Salahaddin University, Erbil, IraqDepartment of Mathematics, College of Science, Salahaddin University, Erbil, IraqDepartment of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, IranSteffensen-type methods with memory were originally designed to solve nonlinear equations without the use of additional functional evaluations per computing step. In this paper, a variant of Steffensen’s method is proposed which is derivative-free and with memory. In fact, using an acceleration technique via interpolation polynomials of appropriate degrees, the computational efficiency index of this scheme is improved. It is discussed that the new scheme is quite fast and has a high efficiency index. Finally, numerical investigations are brought forward to uphold the theoretical discussions.https://www.mdpi.com/2227-7390/7/3/306iterative methodsSteffensen’s methodR-orderwith memorycomputational efficiency |
| spellingShingle | Fuad W. Khdhr Rostam K. Saeed Fazlollah Soleymani Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations Mathematics iterative methods Steffensen’s method R-order with memory computational efficiency |
| title | Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations |
| title_full | Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations |
| title_fullStr | Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations |
| title_full_unstemmed | Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations |
| title_short | Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations |
| title_sort | improving the computational efficiency of a variant of steffensen s method for nonlinear equations |
| topic | iterative methods Steffensen’s method R-order with memory computational efficiency |
| url | https://www.mdpi.com/2227-7390/7/3/306 |
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