5 problems

Consider the high-dimensional integration setting in which the presented method approximates a Riemann sum of the target function within a factor of $1+O(1/n)$ in time…

Let $D_d$ denote the $(d-1)$-dimensional integral considered in the paper, and let $\Delta$ be a positive constant. Bailey et al.'s conjecture. As $d\to\infty$, … Bailey et al. est…

Let $d$ be the dimension, $n$ the number of points in each one-dimensional quadrature rule, $r$ the average tensor-train rank, and $N_{\mathrm{eval}}$ the number of samples evaluat…

Let $C_d$ denote the $(d-1)$-dimensional Ising integral, and define … Let $\gamma$ be the EulerMascheroni constant. Bailey et al.'s conjecture. … The source states that this conjec…

Let $\widetilde{F}_d$ be the class of smooth functions on $[0,1]^d$ defined by … Consider the question whether integration on this class suffers from the curse of dimensionality, a…