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Detalji o izabranom predavanju:
| Seminar: | Seminar za numeričku matematiku i znan. računanje |
| Naziv predavanja: | Extending randomized low-rank approximation techniques to parameter-dependent problems |
| Predavač: | Hei Yin Lam, EPFL Lausanne, Švicarska |
| Vrijeme: |
08.02.2024 12:15 |
| Predavaonica: | 201 |
| Tip: |
Gost seminara |
| Opis: | Randomized algorithms are an increasingly popular approach for performing low-rank approximation and they usually proceed by multiplying the matrix with random dimension reduction matrices (DRMs). Applying such algorithms directly to a matrix $A(t)$ depending on a parameter $t$ in a compact set $D \subset \mathbb{R}^d$ would involve multiplying different, independent DRMs for every $t$, which is not only expensive but also leads to inherently non-smooth approximations. In this talk, we propose to use constant DRMs, that is, $A(t)$ is multiplied with the same DRM for every $t$. The resulting parameter-dependent extensions of two popular randomized algorithms, the randomized singular value decomposition and the generalized Nystr\"{o}m method, are computationally attractive. Therefore, we provide a probabilistic analysis for both algorithms when using Gaussian random DRMs, it shows that our methods reliably return quasi-best low-rank approximations. Furthermore, based on the proposed algorithm, we present an extension to solving the trace estimation problem, which arises from the estimation of spectral densities. Numerical experiments illustrating the properties of the proposed randomized scheme are also presented.
This talk is based upon joint work with Haoze He, Daniel Kressner and Fabio Matti. |
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