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Showing 1 to 4 of 4 for “"Lattice rules"”.
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The structure and average discrepancies of lattice rules for numerical integration
Lattice rules are equal-weight quadrature rules which are used in the approximation of multidimensional integrands over the s-dimensional unit cube [0,1]ˢ. One of the problems encountered in the study of such rules is the unavailability of a unique representation. It is known that any lattice rule …
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Construction of lattice rules for multiple integration based on a weighted discrepancy
… for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to integrals of functions belonging to certain weighted function spaces. These function spaces were proposed as an explanation as to why integrals in many …
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Constructive approaches to quasi-Monte Carlo methods for multiple integration
… recent publications show the existence of lattice rules that satisfy the strong tractability error bounds in weighted Korobov spaces of periodic integrands and weighted Sobolev spaces of non-periodic integrands. However, those results were non-constructive and thus give no clues as to how …
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Qualitative and quantitative convergence results for randomised integration methods
… results by considering randomly shifted lattice rules, randomised (t,d)-sequences, Latin hypercube samples, and randomised Frolov points. Secondly, we study integration w.r.t. probability measures which are available only via their non-normalised density. In this context we investigate …