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Non-optimality of rank-1 lattice sampling in spaces of hybrid mixed smoothness

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      Abstract

      We consider the approximation of functions with hybrid mixed smoothness based on rank-1 lattice sampling. We prove upper and lower bounds for the sampling rates with respect to the number of lattice points in various situations and achieve improvements in the main error rate compared to earlier contributions to the subject. This main rate (without logarithmic factors) is half the optimal main rate coming for instance from sparse grid sampling and turns out to be best possible among all algorithms taking samples on lattices.

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        Optimized general sparse grid approximation spaces for operator equations

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          Spline interpolation on sparse grids

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            Journal
            1510.08336

            Numerical & Computational mathematics

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