论文信息 - Bounds for digital nets and sequences

Bounds for digital nets and sequences

constructions of lowdiscrepancy point sets and sequences, which are of great importance for quasi-Monte Carlo methods in multidimensional numerical integration, are based on the concept of (t,m,s)-nets and (t,s)-sequences. A detailed theory was developed in Niederreiter [9] (see also [10, Chapter 4] for surveys of this theory). So-called digital nets and sequences are of special interest due to the following two reasons. First, until now all construction methods for (t,m,s)nets and (t,s)-sequences which are relevant for applications in quasi-Monte Carlo methods are digital methods over certain rings. Second, digital (t,m,s)-nets behave extremely well for the numerical integration of functions which are representable by an in some sense rapidly converging multivariate Walsh series. In a series of papers, Larcher and several co-authors established lattice rules for the numerical integration of multivariate Walsh series by digital nets. We refer to [5] for a concise introduction in the field of Larcher’s lattice rules. 1.1. Definitions and notations. The concepts of (t,m,s)-nets and of (t,s)-sequences in a base b provide point sets of b m points, respectively infinite sequences, in the half-open s-dimensional unit cube I s := [0, 1) s ,

Wolfgang Ch. Schmid | W. C. Schmid | Reinhard Wolf | R. Wolf

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