Constructive subsampling of finite frames with applications in optimal function recovery
نویسندگان
چکیده
In this paper we present new constructive methods, random and deterministic, for the efficient subsampling of finite frames in Cm. Based on a suitable strategy, are able to extract from any given frame with bounds 0<A≤B<∞ (and condition B/A) similarly conditioned reweighted subframe consisting merely O(mlogm) elements. Further, utilizing deterministic method based principles developed by Batson, Spielman, Srivastava control spectrum sums Hermitian rank-1 matrices, reduce number elements O(m) (with constant close one). By controlling weights via preconditioning step, can, addition, preserve lower bound unweighted case. This permits derivation quasi-optimal (left) Marcinkiewicz-Zygmund inequalities L2(D,ν) constructible node sets size m-dimensional subspaces bounded functions. Those can be applied e.g. (plain) least-squares sampling reconstruction functions, where obtain results avoiding Kadison-Singer theorem. Numerical experiments indicate applicability our results.
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2023
ISSN: ['1096-603X', '1063-5203']
DOI: https://doi.org/10.1016/j.acha.2023.02.004