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      On L2-approximation in Hilbert spaces using function values

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          Abstract

          We study L2-approximation of functions from Hilbert spaces H in which function evaluation is a continuous linear functional, using function values as information. Under certain assumptions on H, we prove that the n-th minimal worst-case error en satisfies enan/log(n),

          where an is the n-th minimal worst-case error for algorithms using arbitrary linear information, i.e., the n-th approximation number. Our result applies, in particular, to Sobolev spaces with dominating mixed smoothness H=Hsmix(Td) with s>1/2 and we obtain ennslogsd(n).
          This improves upon previous bounds whenever d>2s+1.

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          On singular values of matrices with independent rows

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            Linear Approximation

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              Approximation from sparse grids and function spaces of dominating mixed smoothness

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                Author and article information

                Journal
                07 May 2019
                Article
                1905.02516
                5ee3a3d7-9558-4770-ba29-cf5c562b9c44

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                41A25, 41A46, 60B20, 41A63, 46E35
                9 pages
                math.NA math.PR

                Numerical & Computational mathematics,Probability
                Numerical & Computational mathematics, Probability

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