Titlebook: Lattice Rules; Numerical Integratio Josef Dick,Peter Kritzer,Friedrich Pillichshammer Book 2022 The Editor(s) (if applicable) and The Autho

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Josef Dick,Peter Kritzer,Friedrich Pillichshammernterscheidet sich diese Buchreihe von einer rein technologischen Darstellung. Und so m?chte ich zum Ausdruck bringen, wie das Harmonische der Naturge- setze, dem vor allem anderen die übereinstimmung von Struktur und Funktion innewohnt, im hochspezialisierten Individuum Baum und dem der Technik zu-

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Introduction,ter graphics to life sciences, to name just a few areas where integrals or expected values have to be computed. In most cases this cannot be done analytically, and one has to resort to numerical methods. For integrands depending only on one or maybe very few variables there are classical integration

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Integration of Smooth Periodic Functions,c in each variable. Nowadays it is most convenient to examine lattice rules in the context of reproducing kernel Hilbert spaces of smooth and one-periodic functions and to analyze their worst-case errors in this setting. In this chapter we will introduce Korobov spaces, which can be seen as some of

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Modified Construction Schemes, of the resulting generating vectors and an analysis of the runtime of the algorithms. In this chapter we will continue to study this important topic and will present options to fine-tune the CBC construction for various situations and applications. These include the reduced CBC construction, the su