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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Bibliographic Details
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
Subjects:
Derivative-free projection method
Double inertial extrapolation method
Iterative method
Nonlinear equations
Iterative method
Double inertial extrapolation method
Nonlinear equations
Derivative-free projection method
ISSN:0168-9274
Online Access:Get full text
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Summary: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.
ISSN:0168-9274
DOI:10.1016/j.apnum.2024.11.006