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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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          Most cited references 17

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          Quasi-Monte Carlo methods and pseudo-random numbers

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            Optimized general sparse grid approximation spaces for operator equations

             S. Knapek,  M Griebel (2009)
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              Spline interpolation on sparse grids

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                Author and article information

                Journal
                1510.08336

                Numerical & Computational mathematics

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