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- W3040176020 abstract "In this paper, we deal with several aspects of the universal Frolov cubature method, which is known to achieve optimal asymptotic convergence rates in a broad range of function spaces. Even though every admissible lattice has this favorable asymptotic behavior, there are significant differences concerning the precise numerical behavior of the worst-case error. To this end, we propose new generating polynomials that promise a significant reduction in the integration error compared to the classical polynomials. Moreover, we develop a new algorithm to enumerate the Frolov points from non-orthogonal lattices for numerical cubature in the d-dimensional unit cube $$[0,1]^d$$ . Finally, we study Sobolev spaces with anisotropic mixed smoothness and compact support in $$[0,1]^d$$ and derive explicit formulas for their reproducing kernels. This allows for the simulation of exact worst-case errors which numerically validate our theoretical results." @default.
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- W3040176020 date "2020-07-06" @default.
- W3040176020 modified "2023-09-26" @default.
- W3040176020 title "Numerical Performance of Optimized Frolov Lattices in Tensor Product Reproducing Kernel Sobolev Spaces" @default.
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- W3040176020 doi "https://doi.org/10.1007/s10208-020-09463-y" @default.
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