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arXiv · 2607.20732

Algorithm librla: A library of randomized linear algebra routines

Adrianna Gillman·Zydrunas Gimbutas
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Abstract

The library \texttt{librla} is a randomized linear algebra library that is specifically designed for the intermediate-sized matrices (of dimension up to roughly 10,000) that arise in applications such as reduced order modeling, fast direct solvers, least squares solves and, in some settings, data compression. \texttt{librla} is the first software package that is both stable and efficient in several high-level languages: MATLAB, Python and Julia. It also provides increased functionality over existing software. Specifically, it allows the user to choose to create a factorization based on a fixed rank or a desired tolerance. The factorization options include QR, SVD and the interpolative decomposition. Additionally, the factorization can be generated either with access to the matrix or access to a matrix-vector multiplication routine. Numerical results compare the Python implementation with the available PyTorch and SciPy randomized factorizations. Performance of \texttt{librla} in the three languages is comparable.

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Adrianna Gillman, Zydrunas Gimbutas. 2026-07-22. Algorithm librla: A library of randomized linear algebra routines. https://arxiv.org/abs/2607.20732

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