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New Math Paper Details High-Dimensional Euclidean Ball Approximation Rates

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Researchers have established precise bounds on the number of vertices required to approximate a Euclidean unit ball in high dimensions using polytopes. The study reveals that the number of vertices needed grows logarithmically with dimension, specifically $d \log(1 + 1/(\varepsilon\sqrt{d}))$, where $\varepsilon$ is the error tolerance. This work also provides a positive answer to a question regarding subexponential vertex complexity for approximating Euclidean balls and disproves a related extremality principle for unrestricted vertex approximation. AI

RANK_REASON Academic paper on a mathematical topic. [lever_c_demoted from research: ic=1 ai=0.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New Math Paper Details High-Dimensional Euclidean Ball Approximation Rates

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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Yegor Gorodzha, Steven Hoehner, Gil Kur ·

    Approximating the Euclidean Ball by Polytopes: Surprising Rates in High Dimensions

    arXiv:2610.34651v2 Announce Type: cross Abstract: We provide sharp estimates on the number of vertices needed to approximate the Euclidean unit ball $B_d\subset\mathbb R^d$ with relative symmetric-difference volume error at most $\varepsilon\in(0,1)$. We show that the minimum ver…

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