Additive Stability of Frames
Functional Analysis
2025-06-19 v2
Abstract
Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces.
Cite
@article{arxiv.2309.06331,
title = {Additive Stability of Frames},
author = {Oleg Asipchuk and Jacob Glidewell and Luis Rodriguez},
journal= {arXiv preprint arXiv:2309.06331},
year = {2025}
}