@article{e6003073dd354be9a0d907e440c6a6c5,
title = "Conditioning of partial nonuniform Fourier matrices with clustered nodes",
abstract = "We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary {"}off the grid{"} nodes (equivalently, a rectangular Vandermonde matrix with the nodes on the unit circle) in the case when some of the nodes are separated by less than the inverse bandwidth. The bound is polynomial in the reciprocal of the so-called superresolution factor, while the exponent is controlled by the maximal number of nodes which are clustered together. As a corollary, we obtain sharp minimax bounds for the problem of sparse superresolution on a grid under the partial clustering assumptions.",
keywords = "Decimation, Partial Fourier matrix, Prolate matrix, Singular values, Superresolution, Vandermonde matrix with nodes on the unit circle",
author = "Dmitry Batenkov and Laurent Demanet and Gil Goldman and Yosef Yomdin",
note = "Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics",
year = "2020",
doi = "10.1137/18M1212197",
language = "אנגלית",
volume = "41",
pages = "199--220",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "1",
}