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 PillichshammerAccessible introduction for undergraduate students in mathematics or computer science.Discusses practical applications.Explanations of the basic concepts and current methods used in research

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Springer Series in Computational Mathematicshttp://image.papertrans.cn/l/image/581943.jpg

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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 methods which can be applied very successfully.

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上腭

Interferons

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Integration of Smooth Periodic Functions,odic 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 the most classical examples of function classes to which lattice rules for numerical integration have been applied.

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Modified Construction Schemes,and will present options to fine-tune the CBC construction for various situations and applications. These include the reduced CBC construction, the successive coordinate search construction, the projection-corrected CBC construction, and the component-by-component digit-by-digit construction, which all shall be presented here.

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Discrepancy of Lattice Point Sets,r we study the (extreme) discrepancy of lattice point sets and show its relation to the figure of merit .. Based on the latter we obtain efficient constructions of lattice point sets with the almost optimal order of magnitude of discrepancy.

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Integration of Analytic Functions,rule the rate of convergence of the worst-case error is essentially of order . and therefore reflects the smoothness of the reference space. In the cases considered so far, the smoothness parameter . has always been finite and hence we have observed convergence rates of polynomial order.