Journal article 699 views 155 downloads
Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
,
Bilall I. Shaini,
Jamilu Sabi’u,
Abdullah Shah,
Milena J. Petrović ,
Branislav Ivanov ,
Xinwei Cao,
Alena Stupina,
Shuai Li
Algorithms, Volume: 16, Issue: 2, Start page: 64
Swansea University Author:
Shuai Li
-
PDF | Version of Record
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Download (823.47KB)
DOI (Published version): 10.3390/a16020064
Abstract
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...
| Published in: | Algorithms |
|---|---|
| ISSN: | 1999-4893 |
| Published: |
MDPI AG
2023
|
| Online Access: |
Check full text
|
| URI: | https://cronfa.swan.ac.uk/Record/cronfa62798 |
| Abstract: |
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. |
|---|---|
| College: |
Faculty of Science and Engineering |
| Funders: |
Predrag Stanimirović is supported by the Science Fund of the Republic of Serbia, (No. 7750185, Quantitative Automata Models: Fundamental Problems and Applications-QUAM). Predrag Stanimirović acknowledges support Grant No. 451-03-68/2022-14/200124 given by Ministry of Education, Science and Technological Development, Republic of Serbia. Milena J. Petrović acknowledges support Grant No.174025 given by Ministry of Education, Science and Technological Development, Republic of Serbia. Milena J. Petrović acknowledges support from the internal-junior project IJ-0202 given by the Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, Serbia. |
| Issue: |
2 |
| Start Page: |
64 |