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
Main Authors: Ibrahim, Abdulkarim Hassan, Al-Homidan, Suliman
Format: Journal Article
Language:English
Published: 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.
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
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  organization: Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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Keywords Iterative method
Double inertial extrapolation method
Nonlinear equations
Derivative-free projection method
Language English
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SubjectTerms Derivative-free projection method
Double inertial extrapolation method
Iterative method
Nonlinear equations
Title A derivative-free projection method with double inertial effects for solving nonlinear equations
URI https://dx.doi.org/10.1016/j.apnum.2024.11.006
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