A computer search of rank-$2$ lattice rules for multidimensional quadrature

A Computer Search of Rank-2 Lattice Rules for Multidimensional Quadrature

For certain lattice rules of 'rank 2' it has been shown, in a recent paper, that a unique representation exists in a form suitable for computer evaluation. The present paper describes computer searches of such rules, reports results and identifies rules that appear promising for the numerical evaluation of practical multidimensional integrals.

A lower bound for rank 2 lattice rules

We give a lower bound for a quality measure of rank 2 lattice rules which shows that an existence result of Niederreiter is essentially best possible.

Quadrature Rules for Fuzzy Integrals

An application of Diophantine approximation to the construction of rank-1 lattice quadrature rules

Lattice quadrature rules were introduced by Frolov (1977), Sloan (1985) and Sloan and Kachoyan (1987). They are quasi-Monte Carlo rules for the approximation of integrals over the unit cube in Rs and are generalizations of ‘number-theoretic’ rules introduced by Korobov (1959) and Hlawka (1962)— themselves generalizations, in a sense, of rectangle rules for approximating one-dimensional integral...

A Parallel Search for Korobov Lattice Rules

We present results from an extensive parallel search for Korobov lattice rules using the LLL-spectral test with a new normalization strategy. The resulting lattice parameters are distributed via a web-server [9] which provides general information on the spectral test, a database for lattice rule parameters, software for spectral test calculations and related applications, efficient on-line para...