Constructing Good Lattice Rules with Millions of Points

Josef Dick () and Frances Y. Kuo ()
Additional contact information
Josef Dick: University of New South Wales, School of Mathematics
Frances Y. Kuo: University of New South Wales, School of Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2002, 2004, pp 181-197 from Springer

Abstract: Summary We develop an algorithm for the construction of randomly shifted rank-1 lattice rules in d-dimensional weighted Sobolev spaces with a significantly reduced construction cost. The results shown here are an extension of earlier results by the present authors. In this new algorithm, the number of quadrature points n is a product of r distinct prime numbers p 1,…,p r. This allows us to reduce the construction cost to O(n(p 1 + … +p r)d 2), which represents a significant reduction, especially for large n. The constructed rules achieve a worst-case error bound with a rate of convergence of O(n(p 1 + δ p 2 -1/2 ... p r -1/2 ) for any δ > 0. Numerical experiments were carried out for r = 2, 3, 4 and 5. The results demonstrate that it can be advantageous to choose n as a product of up to 5 primes.

Keywords: Prime Number; Generate Vector; Construction Cost; Reproduce Kernel Hilbert Space; Quadrature Point (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18743-8_10

Ordering information: This item can be ordered from
http://www.springer.com/9783642187438

DOI: 10.1007/978-3-642-18743-8_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().