Sharp bounds for non-adaptive randomized approximation of high-dimensional noisy vectors

Robert J. Kunsch; Marcin Wnuk

Sharp bounds for non-adaptive randomized approximation of high-dimensional noisy vectors

Numerical Analysis 2026-07-31 v1

Authors: Robert J. Kunsch , Marcin Wnuk

Abstract

We study the complexity of approximating the finite-dimensional vector space embedding $\ell_p^m \hookrightarrow \ell_q^m$ for $2 \leq p < q \leq \infty$ based on non-adaptive randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance $x \in \mathbb{R}^m$ , where $n \ll m$ . We prove lower bounds on the non-adaptive randomized approximation error with a joint dependence on $(n,m)$ matching previously known upper bounds.

Cite

@article{arxiv.2608.00148,
  title  = {Sharp bounds for non-adaptive randomized approximation of high-dimensional noisy vectors},
  author = {Robert J. Kunsch and Marcin Wnuk},
  journal= {arXiv preprint arXiv:2608.00148},
  year   = {2026}
}