The existence of good extensible rank-1 lattices
Journal of Complexity
On the convergence rate of the component-by-component construction of good lattice rules
Journal of Complexity
Quasi-Monte Carlo methods can be efficient for integration over products of spheres
Journal of Complexity
Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Lattice rule algorithms for multivariate approximation in the average case setting
Journal of Complexity
Intermediate rank lattice rules and applications to finance
Applied Numerical Mathematics
Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Lattice point sets for deterministic learning and approximate optimization problems
IEEE Transactions on Neural Networks
Construction algorithms for higher order polynomial lattice rules
Journal of Complexity
Multidimensional pseudo-spectral methods on lattice grids
Applied Numerical Mathematics
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This paper provides a novel approach to the construction of good lattice rules for the integration of Korobov classes of periodic functions over the unit s-dimensional cube. Theorems are proved which justify the construction of good lattice rules one component at a time - that is the lattice rule for dimension s + 1 is obtained from the rule for dimension s by searching over all possible choices of the (s + 1)th component, while keeping all the existing components unchanged. The construction, which goes against accepted wisdom, is illustrated by numerical examples. The construction is particularly useful if the components of the integrand are ordered, in the sense that the first component is more important than the second, and so on.