2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations
| Format: | General Document |
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| collectionurl | https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 |
| copyright | Copyright©PWB2025 |
| country | Malaysia |
| date | 2017-11-20 |
| format | General Document |
| id | 16159 |
| institution | UniSZA |
| originalfilename | A FAMILY OF CG-TYPE METHODS VIA QUASI-NEWTON UPDATES FOR SOLVING SYMMETRIC SYSTEMS OF NONLINEAR EQUATIONS.pdf |
| person | Dauda Muhammad Kabir |
| recordtype | oai_dc |
| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16159 |
| sourcemedia | Server storage Scanned document |
| spelling | 16159 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16159 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 Server storage Scanned document Universiti Sultan Zainal Abidin UniSZA Private Access UNIVERSITI SULTAN ZAINAL ABIDIN SAMBox 2.4.24; modified using iTextSharp™ 5.5.10 ©2000-2016 iText Group NV (AGPL-version) 168 Copyright©PWB2025 2017-11-20 A FAMILY OF CG-TYPE METHODS VIA QUASI-NEWTON UPDATES FOR SOLVING SYMMETRIC SYSTEMS OF NONLINEAR EQUATIONS.pdf Nonlinear equations—Numerical solutions 2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations The prominent method for solving nonlinear systems of equations is the Newton method, unfortunately this method do have some shortcomings, these includes computation of the Jacobian matrix, solving the Newton system in every iteration, computing and storing an n x n matrix at each iteration which may be difficult, computationally expensive or even impossible to compute for large scale problems. Numerous research and modifications have been done recently to improve the efficiency of these methods. To overcome such drawbacks, a research work is proposed, titled "A Family of CG-T1pe Methods via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations". This is done successfully by modifuing the classical SRI (Symmetric Rank One), DFP (Davidon-Fletcher-Powell), Broyden and PSB (Powell Symmetric Broyden) updates. The attractive attribute of these methods are simple implementation and derivative free approach, thereby require low memory storage. The computational experiment is based on number of iterations, CPU time and residual norm ofF(r2). The code for the methods was done using MATLAB 7.1, R2009b programming environment and run on a personal computer 2.4G112, Intel (R) Core (Tltzt) i7-5500U CPU processor, 4GB RAM memory and on windows XP operator in order to check its efficiency and robustness. For every test problem, different initial points with different dimensions are used, the numerical results are analyzed using the perlormance profile introduced in Dolan and More. By solving several benchmark problerns, the proposed methods are compared with their classical counterparts. The numerical results demonstrate that the proposed methods are fast in terms of CPU time, efficient in terms of number of iterations and effective in approximating the solution. The global convergence properties of the proposed methods are established under appropriate conditions. Dauda Muhammad Kabir Dissertations, Academic Conjugate Gradient (CG) Method Solving Nonlinear Equation Quasi-Newton Updates Thesis |
| spellingShingle | 2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations |
| state | Terengganu |
| subject | Nonlinear equations—Numerical solutions Dissertations, Academic |
| summary | The prominent method for solving nonlinear systems of equations is the Newton method, unfortunately this method do have some shortcomings, these includes computation of the Jacobian matrix, solving the Newton system in every iteration, computing and storing an n x n matrix at each iteration which may be difficult, computationally expensive or even impossible to compute for large scale problems. Numerous research and modifications have been done recently to improve the efficiency of these methods. To overcome such drawbacks, a research work is proposed, titled "A Family of CG-T1pe Methods via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations". This is done successfully by modifuing the classical SRI (Symmetric Rank One), DFP (Davidon-Fletcher-Powell), Broyden and PSB (Powell Symmetric Broyden) updates. The attractive attribute of these methods are simple implementation and derivative free approach, thereby require low memory storage. The computational experiment is based on number of iterations, CPU time and residual norm ofF(r2). The code for the methods was done using MATLAB 7.1, R2009b programming environment and run on a personal computer 2.4G112, Intel (R) Core (Tltzt) i7-5500U CPU processor, 4GB RAM memory and on windows XP operator in order to check its efficiency and robustness. For every test problem, different initial points with different dimensions are used, the numerical results are analyzed using the perlormance profile introduced in Dolan and More. By solving several benchmark problerns, the proposed methods are compared with their classical counterparts. The numerical results demonstrate that the proposed methods are fast in terms of CPU time, efficient in terms of number of iterations and effective in approximating the solution. The global convergence properties of the proposed methods are established under appropriate conditions. |
| title | 2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations |
| title_full | 2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations |
| title_fullStr | 2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations |
| title_full_unstemmed | 2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations |
| title_short | 2017_A Family of CG-Type Methods Via Quasi-Newton Updates for Solving Symmetric Systems of Nonlinear Equations |
| title_sort | 2017_a family of cg-type methods via quasi-newton updates for solving symmetric systems of nonlinear equations |