Optimization of Numerical Algorithms for Solving Large Linear Equation Systems in Industrial Mathematical Computing

M Bastian ; Putry Wahyu Setyaningsih ; Syeda Azwa Asif
International Journal of Applied Mathematics and C... 📅 2024 Vol 1, No 4 🔗 DOI: 10.62951/ijamc.v1i4.275
Abstract
The rapid advancement of modern computing has driven extensive research on numerical algorithms for solving large-scale systems of linear equations. Classical methods such as LU decomposition, Jacobi, and Gauss–Seidel have been revisited and optimized to leverage parallel architectures, GPUs, and even quantum platforms. Recent studies demonstrate that optimized algorithms can reduce computation time by more than 50% while maintaining high accuracy in solving high-dimensional problems. LU decomposition, particularly in its parallel and GPU-based implementations, has shown superior performance in batch processing and industrial-scale simulations. Meanwhile, iterative methods such as Jacobi and Gauss–Seidel remain relevant due to their flexibility in numerical modeling, with further developments for block matrix systems, finite element applications, and FPGA architectures. The integration of these enhanced algorithms is not only beneficial for the advancement of scientific software development but also supports practical applications in engineering simulations, large-scale data optimization, and machine learning. Therefore, an integrative review of modern numerical algorithm developments is crucial in bridging the gap between industrial demands and research progress in scientific computing.
Keywords
Gauss–Seidel; Jacobi; LU decomposition; Numerical computing; Parallel algorithm
How to Cite

M Bastian, et al. (2024). Optimization of Numerical Algorithms for Solving Large Linear Equation Systems in Industrial Mathematical Computing. International Journal of Applied Mathematics and Computing, 1(4). https://doi.org/10.62951/ijamc.v1i4.275

M Bastian; Putry Wahyu Setyaningsih; Syeda Azwa Asif, "Optimization of Numerical Algorithms for Solving Large Linear Equation Systems in Industrial Mathematical Computing," International Journal of Applied Mathematics and Computing, vol. 1, no. 4, 2024.

M Bastian; Putry Wahyu Setyaningsih; Syeda Azwa Asif. "Optimization of Numerical Algorithms for Solving Large Linear Equation Systems in Industrial Mathematical Computing." International Journal of Applied Mathematics and Computing, vol. 1, no. 4, 2024.

M Bastian; Putry Wahyu Setyaningsih; Syeda Azwa Asif. "Optimization of Numerical Algorithms for Solving Large Linear Equation Systems in Industrial Mathematical Computing." International Journal of Applied Mathematics and Computing 1, no. 4 (2024).

M Bastian, et al. (2024) 'Optimization of Numerical Algorithms for Solving Large Linear Equation Systems in Industrial Mathematical Computing', International Journal of Applied Mathematics and Computing, 1(4). doi: 10.62951/ijamc.v1i4.275.

M Bastian; Putry Wahyu Setyaningsih; Syeda Azwa Asif. Optimization of Numerical Algorithms for Solving Large Linear Equation Systems in Industrial Mathematical Computing. International Journal of Applied Mathematics and Computing. 2024;1(4).

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