Tag Archives: higher order polynomial lattice rule

Digital Nets and Sequences Preprint

A complete preprint of the book

is now available here. The final published version can be obtained directly from Cambridge University Press here.

The preprint version differs of course from the final version, for instance, the page numbers are different. However, the numbering of Chapters, Sections, Theorems, Lemmas, Corollaries, Definitions and Examples is the same in both versions. The list of corrections is for the published version. We do not have a separate list for the preprint version (though the corrections for the published version also apply to the preprint version).

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Construction Algorithms for Higher Order Polynomial Lattice Rules

We recently submitted the manuscript

This paper fits into the work on higher order quasi-Monte Carlo rules which started with [22] and [31]. It can be viewed as the higher order extension of [7], where classical polynomial lattice rules were considered.

1. Construction Algorithms

As stated in the title of the manuscript, we present construction algorithms for higher order polynomial lattice rules. The construction is based on the worst-case error rather than the quality parameter {t}. This allows us to find good higher order polynomial lattice rules for weighted function spaces. It also presents a feasible alternative to the direct construction introduced in [31] (and [22] for the periodic case).

We use a variety of approaches to achieve our results. Continue reading