Abstract
Given pointwise samples of an unknown function belonging to a certain model set, one seeks in optimal recovery to recover this function in a way that minimizes the worst-case error of the recovery procedure. While it is often known that such an optimal recovery procedure can be chosen to be linear, e.g., when the model set is based on approximability by a subspace of continuous functions, a construction of the procedure is rarely available. This note uncovers a practical algorithm to construct a linear optimal recovery map when the approximation space is a Chevyshev space of univariate functions that has dimension at least three and contains the constants.
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Funding
S. Foucart is partially supported by grants from the NSF (DMS-2053172) and from the ONR (N00014-20-1-2787).
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Communicated by: Olga Mula
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Foucart, S. Full recovery from point values: an optimal algorithm for Chebyshev approximability prior. Adv Comput Math 49, 57 (2023). https://doi.org/10.1007/s10444-023-10063-x
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DOI: https://doi.org/10.1007/s10444-023-10063-x