Add to ORKGAbstract For periodic integrands with unit period in each variable certain error bounds for lattice rules are conveniently characterised by the gure of merit which was originally introduced in the context of number theoretic rules The problem of nding good rules of orderN that is having N distinct nodes then becomes that of nding rules with large values of This paper presents ecient search methods for the discovery of rank rules and of maximal rank rules of high order which possess good gures of meri
We give an explicit formula for the figure of merit ρN of 2-dimensional rank 2 lattice rules in term...
We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for t...
The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrep...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
Lattice quadrature rules were introduced by Frolov (1977), Sloan (1985) and Sloan and Kachoyan (1987...
The upper class of a lattice rule is a convenient entity for classification and other purposes. The ...
Lattice rules are quasi-Monte Carlo methods for numerical multiple integration that are based on the...
We study the problem of constructing rank- lattice rules which have good bounds on the ``weighted s...
We study the problem of constructing good intermediate-rank lattice rules in the sense of having a l...
AbstractWe develop algorithms to construct rank-1 lattice rules in weighted Korobov spaces of period...
AbstractWe establish results on the worst-case errors that can be achieved by well-chosen lattice ru...
In this paper some of the results of a recent computer search [CoLy99] for optimal three- and four-d...
We introduce a criterion for the evaluation of multidimensional quadrature, or cu-bature, rules for ...
The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driv...
We give an explicit formula for the figure of merit ρN of 2-dimensional rank 2 lattice rules in term...
We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for t...
The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrep...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
Lattice quadrature rules were introduced by Frolov (1977), Sloan (1985) and Sloan and Kachoyan (1987...
The upper class of a lattice rule is a convenient entity for classification and other purposes. The ...
Lattice rules are quasi-Monte Carlo methods for numerical multiple integration that are based on the...
We study the problem of constructing rank- lattice rules which have good bounds on the ``weighted s...
We study the problem of constructing good intermediate-rank lattice rules in the sense of having a l...
AbstractWe develop algorithms to construct rank-1 lattice rules in weighted Korobov spaces of period...
AbstractWe establish results on the worst-case errors that can be achieved by well-chosen lattice ru...
In this paper some of the results of a recent computer search [CoLy99] for optimal three- and four-d...
We introduce a criterion for the evaluation of multidimensional quadrature, or cu-bature, rules for ...
The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driv...
We give an explicit formula for the figure of merit ρN of 2-dimensional rank 2 lattice rules in term...
We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for t...
The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrep...