On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence
A number of optimal order multiple root techniques that require derivative evaluations in the formulas have been proposed in literature. However, derivative-free optimal techniques for multiple roots are seldom obtained. By considering this factor as motivational, here we present a class of optimal...
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| Format: | Article |
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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/7/1091 |
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| author | Janak Raj Sharma Sunil Kumar Lorentz Jäntschi |
| author_facet | Janak Raj Sharma Sunil Kumar Lorentz Jäntschi |
| author_sort | Janak Raj Sharma |
| collection | DOAJ |
| description | A number of optimal order multiple root techniques that require derivative evaluations in the formulas have been proposed in literature. However, derivative-free optimal techniques for multiple roots are seldom obtained. By considering this factor as motivational, here we present a class of optimal fourth order methods for computing multiple roots without using derivatives in the iteration. The iterative formula consists of two steps in which the first step is a well-known Traub–Steffensen scheme whereas second step is a Traub–Steffensen-like scheme. The Methodology is based on two steps of which the first is Traub–Steffensen iteration and the second is Traub–Steffensen-like iteration. Effectiveness is validated on different problems that shows the robust convergent behavior of the proposed methods. It has been proven that the new derivative-free methods are good competitors to their existing counterparts that need derivative information. |
| first_indexed | 2024-03-10T18:42:15Z |
| format | Article |
| id | doaj.art-270885e0a95d45489a4154a7f39ffb15 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:42:15Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-270885e0a95d45489a4154a7f39ffb152023-11-20T05:45:48ZengMDPI AGMathematics2227-73902020-07-0187109110.3390/math8071091On Derivative Free Multiple-Root Finders with Optimal Fourth Order ConvergenceJanak Raj Sharma0Sunil Kumar1Lorentz Jäntschi2Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal Sangrur 148106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal Sangrur 148106, IndiaDepartment of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaA number of optimal order multiple root techniques that require derivative evaluations in the formulas have been proposed in literature. However, derivative-free optimal techniques for multiple roots are seldom obtained. By considering this factor as motivational, here we present a class of optimal fourth order methods for computing multiple roots without using derivatives in the iteration. The iterative formula consists of two steps in which the first step is a well-known Traub–Steffensen scheme whereas second step is a Traub–Steffensen-like scheme. The Methodology is based on two steps of which the first is Traub–Steffensen iteration and the second is Traub–Steffensen-like iteration. Effectiveness is validated on different problems that shows the robust convergent behavior of the proposed methods. It has been proven that the new derivative-free methods are good competitors to their existing counterparts that need derivative information.https://www.mdpi.com/2227-7390/8/7/1091multiple root solverscomposite methodweight-functionderivative-free methodoptimal convergence |
| spellingShingle | Janak Raj Sharma Sunil Kumar Lorentz Jäntschi On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence Mathematics multiple root solvers composite method weight-function derivative-free method optimal convergence |
| title | On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence |
| title_full | On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence |
| title_fullStr | On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence |
| title_full_unstemmed | On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence |
| title_short | On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence |
| title_sort | on derivative free multiple root finders with optimal fourth order convergence |
| topic | multiple root solvers composite method weight-function derivative-free method optimal convergence |
| url | https://www.mdpi.com/2227-7390/8/7/1091 |
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