Component-by-Component Construction of Good Lattice Rules with a Composite Number of Points

✍ Scribed by Frances Y. Kuo; Stephen Joe

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 272 KB
• Volume: 18
• Category: Article
• ISSN: 0885-064X
• DOI: 10.1006/jcom.2002.0650

✦ Synopsis

We develop algorithms to construct rank-1 lattice rules in weighted Korobov spaces of periodic functions and shifted rank-1 lattice rules in weighted Sobolev spaces of non-periodic functions. Analyses are given which show that the rules so constructed achieve strong QMC tractability error bounds. Unlike earlier analyses, there is no assumption that n; the number of quadrature points, be a prime number. However, we do assume that there is an upper bound on the number of distinct prime factors of n: The generating vectors and shifts characterizing the rules are constructed 'component-by-component,' that is, the ðd þ 1Þth components of the generating vectors and shifts are obtained using one-dimensional searches, with the previous d components kept unchanged. # 2002 Elsevier Science (USA)