A derivative-free projection method with double inertial effects for solving nonlinear equations
Recent research has highlighted the significant performance of multi-step inertial extrapolation in a wide range of algorithmic applications. This paper introduces a derivative-free projection method (DFPM) with a double-inertial extrapolation step for solving large-scale systems of nonlinear equati...
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| Published in: | Applied numerical mathematics Vol. 209; pp. 55 - 67 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.03.2025
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| ISSN: | 0168-9274 |
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| Abstract | Recent research has highlighted the significant performance of multi-step inertial extrapolation in a wide range of algorithmic applications. This paper introduces a derivative-free projection method (DFPM) with a double-inertial extrapolation step for solving large-scale systems of nonlinear equations. The proposed method's global convergence is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudo-monotone). This is the first convergence result for a DFPM with double inertial step to solve nonlinear equations. Numerical experiments are conducted using well-known test problems to show the proposed method's effectiveness and robustness compared to two existing methods in the literature. |
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| AbstractList | Recent research has highlighted the significant performance of multi-step inertial extrapolation in a wide range of algorithmic applications. This paper introduces a derivative-free projection method (DFPM) with a double-inertial extrapolation step for solving large-scale systems of nonlinear equations. The proposed method's global convergence is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudo-monotone). This is the first convergence result for a DFPM with double inertial step to solve nonlinear equations. Numerical experiments are conducted using well-known test problems to show the proposed method's effectiveness and robustness compared to two existing methods in the literature. |
| Author | Al-Homidan, Suliman Ibrahim, Abdulkarim Hassan |
| Author_xml | – sequence: 1 givenname: Abdulkarim Hassan orcidid: 0000-0001-5534-1759 surname: Ibrahim fullname: Ibrahim, Abdulkarim Hassan email: ibrahimkarym@gmail.com organization: Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia – sequence: 2 givenname: Suliman orcidid: 0000-0002-5998-0635 surname: Al-Homidan fullname: Al-Homidan, Suliman email: homidan@kfupm.edu.sa organization: Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia |
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| Cites_doi | 10.1007/s10915-023-02311-5 10.1002/nla.2533 10.1090/S0025-5718-06-01840-0 10.1093/imanum/8.1.141 10.1007/s10898-017-0506-0 10.1007/s10898-022-01213-4 10.1016/j.cam.2005.10.002 10.1016/j.apnum.2022.06.015 10.1007/s12190-024-02062-y 10.1016/j.apnum.2022.02.001 10.1007/s11075-022-01356-1 10.1515/dema-2022-0159 10.1002/mma.9033 10.1016/j.apm.2023.01.018 10.1007/s00186-006-0140-y 10.1016/j.orl.2023.07.009 10.1007/s12190-022-01790-3 10.1007/s12190-022-01713-2 10.1007/s10589-023-00513-z 10.1023/A:1011253113155 10.3934/jimo.2023034 10.1080/01630563.2013.812656 10.1002/mma.10159 10.1080/10556780310001610493 10.1137/S1052623494266365 10.1016/j.cam.2007.07.021 10.4134/BKMS.2013.50.3.823 10.1093/imanum/13.3.321 10.1007/s11075-017-0299-8 10.1090/S0025-5718-1974-0343581-1 10.1007/s12190-014-0829-7 10.1080/02331934.2021.2002326 10.1016/j.apnum.2021.02.004 10.1007/s40314-022-02064-1 10.1016/j.cam.2023.115087 10.1137/0723046 10.1002/nla.2471 10.1186/s13660-021-02719-3 10.1007/s00500-022-07536-4 10.3934/jimo.2021173 10.1007/s40314-022-02019-6 10.1007/s10915-021-01657-y 10.1007/s101070100263 10.1137/1019005 |
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| Keywords | Iterative method Double inertial extrapolation method Nonlinear equations Derivative-free projection method |
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| Title | A derivative-free projection method with double inertial effects for solving nonlinear equations |
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