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  • Authors: Dinh Dũng (2012)

  • We study optimal algorithms in adaptive continuous sampling recovery of smooth functions defined on the unit d-cube Id≔[0,1]d. Functions to be recovered are in Besov space . The recovery error is measured in the quasi-norm ‖⋅‖q of . For a set A⊂Lq, we define a sampling algorithm of recovery with the free choice of sample points and recovering functions from A as follows. For each , we choose n sample points which define n sampled values of f. Based on these sample points and sampled values, we choose a function from A for recovering f. The choice of n sample points and a recovering function from A for each defines an n-sampling algorithm . We suggest a new approach to investigate the optimal adaptive sampling recovery by in the sense of continuous non-linear n-widths which...