A new modified conjugate gradient coefficient for solving system of linear equations

• Main Authors: Mustafa, Mamat, Hajar, N., Aini, N, Shapiee, N., Abidin,, Z.Z., Khadijah, W., Rivaie, M
• Format: Conference or Workshop Item
• Language: English
• Published: 2017
• Subjects: HA Statistics; QA Mathematics
• Online Access: http://eprints.unisza.edu.my/1492/1/FH03-FIK-17-10483.jpg; http://eprints.unisza.edu.my/1492/
• Institution: Universiti Sultan Zainal Abidin

Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations