Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated doub...

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Bibliographic Details
Published in:Algorithms 2023-01, Vol.16 (2), p.64
Main Authors: Stanimirović, Predrag S., Shaini, Bilall I., Sabi’u, Jamilu, Shah, Abdullah, Petrović, Milena J., Ivanov, Branislav, Cao, Xinwei, Stupina, Alena, Li, Shuai
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convergence
Convergence (Mathematics)
gradient descent methods
Iterative methods
Jacobian
Methods
Motivation
Nonlinear equations
nonlinear programming
Nonlinear systems
Nonlinear theories
Optimization
Scalars (Mathematics)
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Summary:This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE.
ISSN:1999-4893
1999-4893
DOI:10.3390/a16020064