English

How many continuous measurements are needed to learn a vector?

Numerical Analysis 2024-12-10 v1 Computational Complexity Information Theory Numerical Analysis math.IT

Abstract

One can recover vectors from Rm\mathbb{R}^m with arbitrary precision, using only log2(m+1)+1\lceil \log_2(m+1)\rceil +1 continuous measurements that are chosen adaptively. This surprising result is explained and discussed, and we present applications to infinite-dimensional approximation problems.

Cite

@article{arxiv.2412.06468,
  title  = {How many continuous measurements are needed to learn a vector?},
  author = {David Krieg and Erich Novak and Mario Ullrich},
  journal= {arXiv preprint arXiv:2412.06468},
  year   = {2024}
}

Comments

12 pages

R2 v1 2026-06-28T20:27:51.135Z