We give an explicit formula for the figure of merit ρN of 2-dimensional rank 2 lattice rules in terms of continued fractions for rational numbers. Further we generalize Fibonacci lattice rules to rank 2 Fibonacci lattice rules which have the same ratio of the figure of merit to the number of points as the classical Fibonacci lattice rule
In an earlier paper on differential posets, two lattices Fib(r) and Z(r) were defined for each posit...
We introduce the concept of multiplicity lattices of $2$-multiarrangements, and determine the behav...
Abstract. The continuing and widespread use of lattice rules for high-dimensional numerical quadratu...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
Abstract For periodic integrands with unit period in each variable certain error bounds for lattic...
We study the trigonometric degree of pairs of embedded cubature rules for the approximation of two-d...
Lattice quadrature rules were introduced by Frolov (1977), Sloan (1985) and Sloan and Kachoyan (1987...
We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for t...
We study the trigonometric degree of pairs of embedded cubature rules for the approximation of two-d...
We study the trigonometric degree of pairs of embedded cubature rules for the approximation of two-d...
The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driv...
Lattice rules are quasi-Monte Carlo methods for numerical multiple integration that are based on the...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
We introduce a criterion for the evaluation of multidimensional quadrature, or cu-bature, rules for ...
The upper class of a lattice rule is a convenient entity for classification and other purposes. The ...
In an earlier paper on differential posets, two lattices Fib(r) and Z(r) were defined for each posit...
We introduce the concept of multiplicity lattices of $2$-multiarrangements, and determine the behav...
Abstract. The continuing and widespread use of lattice rules for high-dimensional numerical quadratu...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
Abstract For periodic integrands with unit period in each variable certain error bounds for lattic...
We study the trigonometric degree of pairs of embedded cubature rules for the approximation of two-d...
Lattice quadrature rules were introduced by Frolov (1977), Sloan (1985) and Sloan and Kachoyan (1987...
We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for t...
We study the trigonometric degree of pairs of embedded cubature rules for the approximation of two-d...
We study the trigonometric degree of pairs of embedded cubature rules for the approximation of two-d...
The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driv...
Lattice rules are quasi-Monte Carlo methods for numerical multiple integration that are based on the...
AbstractFor periodic integrands with unit period in each variable, certain error bounds for lattice ...
We introduce a criterion for the evaluation of multidimensional quadrature, or cu-bature, rules for ...
The upper class of a lattice rule is a convenient entity for classification and other purposes. The ...
In an earlier paper on differential posets, two lattices Fib(r) and Z(r) were defined for each posit...
We introduce the concept of multiplicity lattices of $2$-multiarrangements, and determine the behav...
Abstract. The continuing and widespread use of lattice rules for high-dimensional numerical quadratu...
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