The first two worst erasure patterns in Fourier sampling at fixed codimension
Year: 2026
Type: preprint
Abstract: For fixed integers 2 <= r <= ell, we retain M-ell consecutive frequencies of the unnormalized Fourier matrix of order M and erase any r sampling rows. For all sufficiently large M, we identify the first two minima of the squared least singular value over all erasure sets, including sets depending on M. The minimum occurs exactly at cyclically consecutive erasures. After excluding these, the minimum occurs at translates and reflections of {0,2,3,...,r}. Both values have explicit leading constants and relative error O(M^-2), and their leading ratio depends only on r. The results also determine the worst least-squares noise amplification and spectral condition number.
Author: Xu, Zihuan
Institution: Capital Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223475556
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