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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Random sections of ellipsoids and the power of random information
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If you have a question about this talk, please contact info@newton.ac.uk. ASCW01 - Challenges in optimal recovery and hyperbolic cross approximation We study the circumradius of the intersection of an $m$-dimensional ellipsoid$\mathcal E$ with half axes $\sigma_1\geq\dots\geq \sigma_m$ with random subspaces of codimension $n$. We find that, under certain assumptions on $\sigma$, this random radius $\mathcal{R}n=\mathcal{R}_n(\sigma)$ is of the same order as the minimal such radius $\sigma{n+1}$ with high probability. In other situations $\mathcal{R}_n$ is close to the maximum$\sigma_1$. The random variable $\mathcal{R}_n$ naturally corresponds to the worst-case error of the best algorithm based on random information for $L_2$-approximation of functions from a compactly embedded Hilbert space $H$ with unit ball $\mathcal E$. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:
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