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cs.DS2026
Quasi-Monte Carlo Beyond Hardy-Krause II: Samples Suffice
Ekene Ezeunala, Agastya Vibhuti Jha, Haotian Jiang
Numerical integration studies how well one can estimate the integral of a function over using sample points. The two classical methods, Monte Carlo (MC) and quasi…
cs.DS2026
A Simpler Analysis of the Bansal-Jiang Quasi Monte-Carlo Algorithm via Haar Wavelets
Jiaheng Chen, Agastya Vibhuti Jha, Haotian Jiang
Numerical integration---approximating the integral of a function using point evaluations---is a central task in science and engineering. The two main paradigms for this pro…
cs.DS2026
Near-Optimal Constructive Bounds for Prefix Discrepancy and Steinitz Problems via Affine Spectral Independence
Kunal Dutta, Agastya Vibhuti Jha, Haotian Jiang
A classical result of Steinitz from 1913 \cite{Ste13}, answering an earlier question of Riemann and Lévy (e.g., \cite{Lev05}), states that for any norm in $\mathbb{R}^d…