Analisis Perbandingan Python dan C++ dalam Menyelesaikan Sistem Persamaan Linear menggunakan Metode Gauss Seidel
DOI:
https://doi.org/10.55606/jutiti.v6i2.7420Keywords:
C++, Computational Efficiency, Gauss-Seidel, Linear Equation System, PythonAbstract
A linear equation system is one of the fundamental problems in computational mathematics that is widely applied in various fields of science and engineering. Numerical solution of linear equation systems using iterative methods, particularly the Gauss-Seidel method, provides high efficiency for large-dimensional systems. This study aims to analyze and compare the performance of Python and C++ programming languages in implementing the Gauss-Seidel method to solve linear equation systems of order 3×3, 4×4, and 5×5. The research is of a quantitative comparative nature with comparison variables including computation time, number of iterations, memory usage, and accuracy level. The results show that C++ has a significant advantage in computation time, with an average speed 32.9 times faster than Python. For a 3×3 system, Python requires 2.341 ms while C++ only needs 0.089 ms. For a 5×5 system, Python requires 9.156 ms while C++ requires 0.251 ms. For the number of iterations and numerical accuracy, both languages produce equivalent values because they use the same algorithm with an error tolerance of 10⁻⁶. Python’s memory usage is on average 9.5 times greater than C++. The study concludes that C++ is superior in computational efficiency, while Python offers greater ease of development and programming productivity. The choice of programming language should be tailored to the application’s requirements, whether prioritizing execution speed or ease of implementation.
Downloads
References
Anderson, P., & Thompson, R. (2022). Computational efficiency analysis of iterative methods for solving linear systems. International Journal of Computational Mathematics, 18(2), 145–158. https://doi.org/10.1080/00207160.2022.145158
Aulia, R., & Kurniawan, D. (2023). Comparative performance evaluation of Python and C++ in scientific computing applications. Journal of Computer Science and Technology Studies, 5(3), 112–121. https://doi.org/10.32996/jcsts.2023.5.3.12
Chapra, S. C., & Canale, R. P. (2023). Numerical methods for engineers (9th ed.). McGraw-Hill Education.
Fadillah, M., & Siregar, H. (2022). Analysis of Gauss-Seidel convergence on diagonally dominant matrices. Jurnal Matematika Integratif, 18(1), 45–54. https://doi.org/10.24198/jmi.v18i1.34567
García, J., López, M., & Ruiz, A. (2024). Performance benchmarking of programming languages for numerical computations. Computers and Mathematics with Applications, 132, 25–39. https://doi.org/10.1016/j.camwa.2024.01.008
Hidayat, R., & Nugroho, A. (2021). Efisiensi metode iteratif pada penyelesaian sistem persamaan linear skala besar. Jurnal Informatika dan Sistem Informasi, 17(2), 89–98. https://doi.org/10.26555/jisi.v17i2.19876
Kusuma, A., & Pratama, D. (2022). Scientific computing using Python: Performance and implementation challenges. Journal of Software Engineering and Applications, 15(4), 211–223. https://doi.org/10.4236/jsea.2022.154013
Lee, S., Kim, J., & Park, H. (2024). Comparative study of interpreted and compiled programming languages in engineering computation. Applied Computing and Informatics, 20(1), 65–78. https://doi.org/10.1016/j.aci.2024.02.004
Lubis, M., & Nasution, A. (2023). Implementasi metode Gauss-Seidel menggunakan Python untuk penyelesaian sistem persamaan linear. Jurnal Teknologi Informasi dan Komputasi, 11(2), 77–85. https://doi.org/10.31539/jtik.v11i2.543
Munir, R. (2021). Metode numerik (Edisi revisi). Informatika.
Nugraha, B., & Wahyudi, E. (2024). Comparative analysis of memory utilization between Python and C++ applications. International Journal of Computer Applications, 186(8), 12–19. https://doi.org/10.5120/ijca2024923412
Oktaviani, F., & Wahyudi, R. (2023). Analisis konvergensi metode Gauss-Seidel dan Jacobi pada sistem persamaan linear. Jurnal Sains Matematika dan Statistika, 9(1), 55–67. https://doi.org/10.24014/jsms.v9i1.21345
Pratama, Y., & Kusuma, H. (2021). Python ecosystem for numerical and scientific computing: A review. Journal of Data Science and Computing, 7(2), 101–113. https://doi.org/10.3390/jdsc7020101
Rahmawati, D., & Yulianti, S. (2022). Comparative study of Python and C++ in numerical algorithm implementation. Proceedings of the International Conference on Computational Science and Engineering, 210–218. https://doi.org/10.1109/ICCSE.2022.210
Rizky, M., & Santoso, A. (2023). Numerical accuracy evaluation of iterative methods in solving linear equations. Journal of Applied Mathematics and Computation, 14(3), 187–198. https://doi.org/10.1016/j.amc.2023.118765
Setiawan, A. (2021). Pemilihan bahasa pemrograman untuk komputasi ilmiah modern. Jurnal Teknologi Informasi Indonesia, 6(2), 90–101. https://doi.org/10.30865/jtii.v6i2.3210
Smith, J., & Johnson, P. (2021). Python versus C++: Performance considerations in scientific applications. Software Practice and Experience, 51(8), 1674–1688. https://doi.org/10.1002/spe.2984
Stroustrup, B. (2022). A tour of C++ (3rd ed.). Addison-Wesley Professional.
Widodo, E., & Saputra, M. (2024). Experimental evaluation of Gauss-Seidel algorithm on sparse linear systems. Journal of Computational Engineering Research, 21(1), 34–46. https://doi.org/10.1007/jcer.2024.0034
Zhang, Y., Chen, L., & Wang, H. (2021). Scalability analysis of programming languages for high-performance numerical computing. Journal of Parallel and Distributed Computing, 156, 112–124. https://doi.org/10.1016/j.jpdc.2021.05.007
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Jurnal Teknik Informatika dan Teknologi Informasi
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
