Speaker
Description
The randomized singular value decomposition proposed in [1] has certainly become one of the most well-established randomization-based algorithms in numerical linear algebra. The key ingredient of the entire procedure is the computation of a subspace which is close to the column space of the target matrix $\mathbf{A}$ up to a certain probabilistic confidence. In our work [2] we propose a modification to the standard randomized SVD procedure which leads, in general, to better approximations to $\text{Range}(\mathbf{A})$ at the same computational cost. To this end, we explicitly construct information from the row space of $\mathbf{A}$ enhancing the quality of our approximation. We also observe that very few pieces of information from $\text{Range}(\mathbf{A}^T)$ are indeed necessary. We thus design a variant of our algorithm equipped with a subsampling step which largely increases the efficiency of our procedure while attaining competitive accuracy records.
Our findings are supported by both theoretical analysis and numerical results.
- N. Halko, P. G. Martinsson, and J. A. Tropp. Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions. SIAM Review \textbf{53.2}, 217–288 (2011). DOI: 10.1137/090771806
- Davide Palitta and Sascha Portaro. Row-aware Randomized SVD with applications. arXiv: 2408.04503 [math.NA] (2024). URL: https://arxiv.org/abs/2408.04503.
