2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations
| Format: | General Document |
|---|
| _version_ | 1860798154737188864 |
|---|---|
| building | INTELEK Repository |
| collection | Online Access |
| collectionurl | https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 |
| copyright | Copyright©PWB2025 |
| country | Malaysia |
| date | 2018-09-03 |
| format | General Document |
| id | 16208 |
| institution | UniSZA |
| originalfilename | NEW CONJUGATE GRADIENT METHODS AND THEIR APPLICATION FOR SOLVING SYSTEM OF LINEAR EQUATIONS (PHD_2018).pdf |
| person | Nurul Hajar Binti Mohd Yussoff |
| recordtype | oai_dc |
| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16208 |
| sourcemedia | Server storage Scanned document |
| spelling | 16208 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16208 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 General Document Malaysia Library Staff (Top Management) Library Staff (Management) Library Staff (Support) Terengganu Faculty of Informatics & Computing English application/pdf 1.5 227 Server storage Scanned document Universiti Sultan Zainal Abidin UniSZA Private Access UNIVERSITI SULTAN ZAINAL ABIDIN SAMBox 2.3.4; modified using iTextSharp™ 5.5.10 ©2000-2016 iText Group NV (AGPL-version) Copyright©PWB2025 2018-09-03 Conjugate gradient methods NEW CONJUGATE GRADIENT METHODS AND THEIR APPLICATION FOR SOLVING SYSTEM OF LINEAR EQUATIONS (PHD_2018).pdf Nurul Hajar Binti Mohd Yussoff Iterative Methods Numerical Linear Algebra 2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations In mathematics, conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. The CG method is easy to implement due to its simplicity and is proven to be effective in solving real practical application. The linear system Ax b is solved by the CG method iteratively. Although the field has received much specialized attention in recent years, some of new approaches of CG methods cannot surpass the efficiency of the previous version of CG methods. Therefore, in this research, two new CG methods, NHMR and NHMR* methods based on researcher’s name (Nurul Hajar, Mustafa and Rivaie) which retain the global convergence of the original CG methods are proposed. These new methods are tested based on number of iterations and CPU time. The efficiency of the new CG methods is studied by testing on 25 standard test problems of unconstrained optimization functions. For every test problem, four different initial points have been used ranging from the one that is closer to the solution point to the one that is furthest, which leads to the proof of global convergence properties. These test problems are computed using Matlab program on Acer Aspire V5 Intel Core i5 with 1.80 GHz and 4 GB RAM. Numerical results are analyzed using the performance profile suggested by Dolan and More. The NHMR and NHMR* methods are compared to the well-known previous CG methods, Fletcher-Reeeves (FR), Polak Ribiere (PRP), Wei-Yao-Liu (WYL) and Dai-Wen (DPRP) using exact and inexact line searches. It is proven that these new methods satisfy sufficient descent conditions and global convergence properties. It is necessary for these proposed methods to converge with an optimized CPU time consumption. Based on the results, NHMR and NHMR* methods have the highest percentage in solving all test problems compared to the FR, PRP, WYL and DPRP methods. Both new methods are able to lessen the number of iterations and central processing times per unit. This research also shows some real application of these newly proposed methods to solve system of linear equations. Hence, it can be concluded that these new proposed methods perform well for solving unconstrained optimization problems and also system of linear equations. Dissertations, Academic Conjugate Gradient Methods Thesis |
| spellingShingle | 2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations |
| state | Terengganu |
| subject | Conjugate gradient methods Dissertations, Academic |
| summary | In mathematics, conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. The CG method is easy to implement due to its simplicity and is proven to be effective in solving real practical application. The linear system Ax b is solved by the CG method iteratively. Although the field has received much specialized attention in recent years, some of new approaches of CG methods cannot surpass the efficiency of the previous version of CG methods. Therefore, in this research, two new CG methods, NHMR and NHMR* methods based on researcher’s name (Nurul Hajar, Mustafa and Rivaie) which retain the global convergence of the original CG methods are proposed. These new methods are tested based on number of iterations and CPU time. The efficiency of the new CG methods is studied by testing on 25 standard test problems of unconstrained optimization functions. For every test problem, four different initial points have been used ranging from the one that is closer to the solution point to the one that is furthest, which leads to the proof of global convergence properties. These test problems are computed using Matlab program on Acer Aspire V5 Intel Core i5 with 1.80 GHz and 4 GB RAM. Numerical results are analyzed using the performance profile suggested by Dolan and More. The NHMR and NHMR* methods are compared to the well-known previous CG methods, Fletcher-Reeeves (FR), Polak Ribiere (PRP), Wei-Yao-Liu (WYL) and Dai-Wen (DPRP) using exact and inexact line searches. It is proven that these new methods satisfy sufficient descent conditions and global convergence properties. It is necessary for these proposed methods to converge with an optimized CPU time consumption. Based on the results, NHMR and NHMR* methods have the highest percentage in solving all test problems compared to the FR, PRP, WYL and DPRP methods. Both new methods are able to lessen the number of iterations and central processing times per unit. This research also shows some real application of these newly proposed methods to solve system of linear equations. Hence, it can be concluded that these new proposed methods perform well for solving unconstrained optimization problems and also system of linear equations. |
| title | 2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations |
| title_full | 2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations |
| title_fullStr | 2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations |
| title_full_unstemmed | 2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations |
| title_short | 2018_New Conjugate Gradient Methods And Their Application for Solving System of Linear Equations |
| title_sort | 2018_new conjugate gradient methods and their application for solving system of linear equations |