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- W4286758962 abstract "AbstractIn Chapter 2 we introduced the Korobov spaces ({mathcal{H}}_{{{text{kor}},d,alpha ,gamma }}) and studied numerical integration using lattice rules for these spaces. The parameter (alpha) is related to the smoothness of the elements of ({mathcal{H}}_{{{text{kor}},d,alpha ,gamma }}) (see Propositions 2.2 and 2.4) and is called the smoothness parameter of these spaces. For an optimal integration rule the rate of convergence of the worst-case error is essentially of order (O(N^{ - alpha } )) and therefore reflects the smoothness of the reference space. In the cases considered so far, the smoothness parameter (alpha) has always been finite and hence we have observed convergence rates of polynomial order." @default.
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- W4286758962 date "2022-01-01" @default.
- W4286758962 modified "2023-09-23" @default.
- W4286758962 title "Integration of Analytic Functions" @default.
- W4286758962 doi "https://doi.org/10.1007/978-3-031-09951-9_9" @default.
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