Mario Ullrich, Peter Kritzer, Dirk Nuyens, Frances Y. Kuo,
"Lattice rules with random n achieve nearly the optimal O(n???1/2) error independently of the dimension"
, in Journal of Approximation Theory, Vol. 240, Seite(n) 96-113, 2019, ISSN: 0021-9045
Original Titel:
Lattice rules with random n achieve nearly the optimal O(n???1/2) error independently of the dimension
Sprache des Titels:
Englisch
Original Kurzfassung:
This paper is a significant advancement over previous related works with respect to the potential for implementation and the independence of error bounds on the problem dimension. Other known algorithms which achieve the optimal error bounds, such as those based on Frolov?s method, are very difficult to implement especially in high dimensions. Here we adapt a lesser-known randomization technique introduced by Bakhvalov in 1961. This algorithm is based on rank-1 lattice rules which are very easy to implement given the integer generating vectors. A simple probabilistic approach can be used to obtain suitable generating vectors.