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Numerical Linear Algebra: Applications in Machine Learning Using Python

Supraja S

RV PU College, Jayanagar

87-92

Vol: 15, Issue: 4, 2025

Receiving Date: 2025-09-30 Acceptance Date:

2025-10-24

Publication Date:

2025-10-29

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http://doi.org/10.37648/ijrst.v15i04.006

Abstract

Modern machine learning is, at its core, large-scale numerical linear algebra (NLA): multiplying matrices, solving least-squares systems, computing eigenvectors/SVDs, and approximating kernels efficiently. As datasets and model sizes grow, classical “exact” methods often become too slow or too memory-heavy, making randomized and iterative NLA essential. This paper surveys where NLA appears in machine learning pipelines, which algorithms matter most (direct, iterative, and randomized), and how Python practitioners implement them using NumPy/SciPy and GPU-enabled frameworks. We also include a comparative analysis that connects algorithmic choices to accuracy, runtime, and scalability.

Keywords: machine learning; NLA; SVDs; NumPy/SciPy and GPU-enabled

References

  1. Calandriello, D., Lazaric, A., & Valko, M. (2017). Analysis of Nyström method with sequential ridge leverage score sampling. In Proceedings of the 34th International Conference on Machine Learning (Vol. 70, pp. 1832- 1840). PMLR.
  2. Gower, R. M., & Richtárik, P. (2017). Randomized iterative methods for linear systems. SIAM Journal on Matrix Analysis and Applications, 38(2), 511–544. https://doi.org/10.1137/15M1025487
  3. Kressner, D., Steinlechner, M., & Vandereycken, B. (2016). Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure. SIAM Journal on Scientific Computing, 38(4), A2018– A2044. https://doi.org/10.1137/15M1032909
  4. Martinsson, P.-G., & Tropp, J. A. (2020). Randomized numerical linear algebra: Foundations and algorithms. Acta Numerica, 29, 403–572. https://doi.org/10.1017/S0962492920000021
  5. Raschka, S., Patterson, J., & Nolet, C. (2020). Machine learning in Python: Main developments and technology trends in data science, machine learning, and artificial intelligence. Information, 11(4), 193. https://doi.org/10.3390/info11040193
  6. Sankaran, A., Alashti, N. A., & Psarras, C. (2022). Benchmarking the linear algebra awareness of TensorFlow and PyTorch. arXiv. https://doi.org/10.48550/arXiv.2202.09888
  7. Wang, Z., & Mahoney, M. W. (2025). On the noise sensitivity of the randomized SVD. IEEE Transactions on Information Theory, 71(5), 3642–3657. https://doi.org/10.1109/TIT.2024.3450412
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