An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix - Khadizah Ghazali; Jumat Sulaiman; Yosza Dasril; Darmesah Gabda (2020)
In large-scale problems, classical Newton’s method requires solving a large linear system of equations resulting from determining the Newton direction. This process often related as a very complicated process, and it requires a lot of computation (either in time calculation or memory requirement per iteration). Thus to avoid this problem, we proposed an improved way to calculate the Newton direction using an Accelerated Overrelaxation (AOR) point iterative method with two different parameters. To check the performance of our proposed Newton’s direction, we used the Newton method with AOR iteration for solving unconstrained optimization problems with its Hessian is in arrowhead form and compared it with a combination of the Newton method with Gauss-Seidel (GS) iteration and the Newton method with Successive Over Relaxation (SOR) iteration. Finally, comparison results show that our proposed technique is significantly more efficient and more reliable than reference methods.