Papers › Constructive subsampling of finite frames with applications in optimal function recovery
Constructive subsampling of finite frames with applications in optimal function recovery
Felix Bartel, Martin Schäfer, Tino Ullrich
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In this paper we present new constructive methods, random and deterministic, for the efficient subsampling of finite frames in ℂᵐ. Based on a suitable random subsampling strategy, we are able to extract from any given frame with bounds 0<A≤B<∞ (and condition B/A) a similarly conditioned reweighted subframe consisting of merely 𝒪(mlogm) elements. Further, utilizing a deterministic subsampling method based on principles developed by Batson, Spielman, and Srivastava to control the spectrum of sums of Hermitian rank-1 matrices, we are able to reduce the number of elements to 𝒪(m) (with a constant close to one). By controlling the weights via a preconditioning step, we can, in addition, preserve the lower frame bound in the unweighted case. This permits the derivation of new quasi-optimal unweighted (left) Marcinkiewicz-Zygmund inequalities for L₂(D,ν) with constructible node sets of size 𝒪(m) for m-dimensional subspaces of bounded functions. Those can be applied e.g. for (plain) least-squares sampling reconstruction of functions, where we obtain new quasi-optimal results avoiding the Kadison-Singer theorem. Numerical experiments indicate the applicability of our results.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections