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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Lattice Rules in the Randomized Setting, We present a randomized algorithm . for numerical integration of elements of the weighted Korobov space . that uses at most . integration nodes and that is based on rank-1 lattice rules as building blocks.

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Stability of Lattice Rules, it for a space with different parameters? Do we still get a fast rate of convergence? In other words, we ask whether lattice rules are stable with respect to a change of parameters. In the following we provide some results in this direction.

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,,,, functions in the Korobov space in the .-norm. Obviously, .-approximation is in general a much more difficult task than .-approximation, so it is, a priori, not clear whether lattice rules can help also in the more demanding .-case. This is an interesting problem, and there are several results showi

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Multiple Rank-1 Lattice Point Sets,proximation than when using ordinary rank-1 lattice point sets (see Chapters .and.). The basic idea of multiple lattice point sets is to consider the “union” of several rank-1 lattice point sets and to use them suitably in an approximation algorithm. In order to find good multiple lattice point sets

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Josef Dick,Peter Kritzer,Friedrich Pillichshammermerika; diese Baumriesen erreichen ein Alter von zirka 500 Jahren, eine Höhe bis 380 Fuß engl., einen Durchmesser bis 15 Fuß engl., und einige haben einen Kubikinhalt von 142 cbm aufgewiesen. In gewissen Gegenden erreichen ganze Waldungen eine Durchschnittshöhe von 250 Fuß und der Durchschnittsdurch