##plugins.themes.bootstrap3.article.main##

Ferdinan Rinaldo Tampubolon
Sinta Marito Siagian
Samaria Chrisna
Rischa Devita
Indah Nurhidayati

Abstract

System of Linear Equation  where  is a non-singular and square matrix .  Method for solving System of Linear Equation consist of direct method and indirect method. Further indirect methods were divided into two, that is stationary and non-stationary. This research will conduct a comparative study of several indirect methods and direct methods in solving several cases of Linear equation systems. Some methods that will be compared in this research are jacobi, gauss-seidel, SOR, conjugate and biconjugate gradient. Testing several methods for some kind of matrix is useful to understand the characteristics of each method in solving different types of matrices. The result show that non-stationary such as conjugate and biconjugate has a less computation and faster to convergence compared to stationary method for several symmetric and non-symmetric matrices

##plugins.themes.bootstrap3.article.details##

How to Cite
Tampubolon, F. R., Siagian, S. M., Chrisna, S., Devita, R., & Nurhidayati, I. (2023). Stationary and non-stationary method for solving system of linear equation. International Journal of Basic and Applied Science, 12(1), 10–19. https://doi.org/10.35335/ijobas.v12i1.173
References
J. C. Butcher, The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods. Wiley-Interscience, 1987.
N. Nurullaeli, "Media Analisis Rangkaian Listrik Menggunakan Pendekatan Numerik Gauss-Jordan, Gauss-Seidel, dan Cramer," Navigation Physics: Journal of Physics Education, vol. 2, no. 1, pp. 1-8, 2020.
I. Hamid, "Balancing Chemical Equations by Systems of Linear Equations," Applied Mathematics, vol. 10, no. 7, pp. 521-526, 2019.
R. Saikia and D. Sarma, "A Case study on an Economic problem by using Fuzzy linear Equations," IJSRSET, vol. 1, no. 6, pp. 391-394, 2015.
A. Mandal, B. Cherukuru, and P. Y. Rani, "A STUDY OF INVESTIGATING THE BEST METHOD TO SOLVE LINEAR SYSTEM OF EQUATIONS AND ITS APPLICATIONS."
L. N. Trefethen and D. Bau, Numerical linear algebra. Siam, 2022.
S. W. a. N. X. Haoyu Luo, "Three methods for solving systems of linear equations: Comparing the advantages and disadvantages," Journal of Physics: Conference Series, vol. 2012, 2021.
R. Khan, S. Gharib, and S. R. Ali, "System of linear equations, Guassian elimination," Global Journal of Computer Science and Technology, vol. 15, no. C5, pp. 23-26, 2015.
R. Mittal and A. Al-Kurdi, "Application of the Cramer rule in the solution of sparse systems of linear algebraic equations," Journal of computational and applied mathematics, vol. 136, no. 1-2, pp. 1-15, 2001.
S. A. Meligy and I. Youssef, "Relaxation parameters and composite refinement techniques," Results in Applied Mathematics, vol. 15, p. 100282, 2022.
F. Aryani and L. T. Lestari, "Metode Gauss-Seidel dan Generalisasi Gauss-Seidel untuk Menyelesaikan Sistem Persamaan Linear Kompleks (Contoh Kasus: SPL Kompleks dengan 4 persamaan dan 4 variabel)," Jurnal Sains Matematika dan Statistika, vol. 2, no. 2, pp. 21-31, 2016.
A. Ramadhan and A. Sirait, "Generalisasi metode Gauss-Seidel Untuk Menyelesaikan Sistem Persamaan Linear," Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam, vol. 1, no. 2, p. 8, 2014.
T. Mayooran and E. Light, "Applying the successive over-relaxation method to a real world problems," American Journal of Applied Mathematics and Statistics, vol. 4, no. 4, pp. 113-117, 2016.
S. Zhu, L. Wu, P. Cheng, and J. Zhou, "Application of modified iterative method to simulate rainfall infiltration in unsaturated soils," Computers and Geotechnics, vol. 148, p. 104816, 2022.
G. Dessalew, "Some Modified Stationary and Non-Stationary Iterative Methods for Solving System of Linear Equations," 2022.
S. G. Shareef and D. A. Sulaiman, "Conjugate Gradient Method for System of Linear Algebraic Equations," Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 12, no. 14, pp. 5854-5865, 2021.
G. Ortega, E. M. Garzón, F. Vázquez, and I. García, "The BiConjugate gradient method on GPUs," The Journal of Supercomputing, vol. 64, pp. 49-58, 2013.
H. Ping, Y. Wang, C. Wei, J. Xi, T. Zhang, and Y. Gao, "DCG: An efficient Distributed Conjugate Gradient algorithm for solving linear equations in multi-agent networks," Results in Control and Optimization, vol. 10, p. 100213, 2023.
P. J. Martinez-Ferrer, T. Arslan, and V. Beltran, "Improving the performance of classical linear algebra iterative methods via hybrid parallelism," Journal of Parallel and Distributed Computing, 2023.
M. Tiwari and S. Vadhiyar, "Pipelined Preconditioned Conjugate Gradient Methods for real and complex linear systems for distributed memory architectures," Journal of Parallel and Distributed Computing, vol. 163, pp. 147-155, 2022.
A. Bakari and I. Dahiru, "Comparison of Jacobi and Gauss-Seidel iterative methods for the solution of systems of linear equations," Asian Research Journal of Mathematics, vol. 8, no. 02, p. 2018, 2018.
S. Karunanithi, N. Gajalakshmi, M. Malarvishi, and M. Saileshwari, "A Study on comparison of Jacobi, Gauss-Seidel and SOR methods for the solution in system of linear equations," Int. J. of Math. Trends and Technology,(IJMTT), vol. 56, no. 4, 2018.
H. Ibrahim, H. Chinwenyi, and H. Ude, "On the Algorithmic Iterative Solutions of Conjugate Gradient, Gauss-Seidel and Jacobi Methods for Solving Systems of Linear Equations," International Journal of Mathematical and Computational Sciences, vol. 15, no. 11, pp. 113-118, 2021.
K. HarpinderKaur, "Convergence of Jacobi and Gauss-Seidel Method and Error Reduction Factor," IOSR Journal of Mathematics (IOSRJM), 2012.
P. Wang, S. Mou, J. Lian, and W. Ren, "Solving a system of linear equations: From centralized to distributed algorithms," Annual Reviews in Control, vol. 47, pp. 306-322, 2019.
P. S. S.P. Venkateshan, P. S. S.P. Venkateshan, Ed. Computational Methods in Engineering (Chapter 2 - Solution of Linear Equations,). Academic Press, 2014.
A. El Akkraoui, Y. Trémolet, and R. Todling, "Preconditioning of variational data assimilation and the use of a bi‐conjugate gradient method," Quarterly Journal of the Royal Meteorological Society, vol. 139, no. 672, pp. 731-741, 2013.
O. T. Olu, "On The Direct and Indirect Methods of Solving Systems of Linear Equations " Scholars Journal of Physics, Mathematics and Statistics 2018.