Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Intermediate rank lattice rules for multidimensional integration
SIAM Journal on Numerical Analysis
Component-by-component construction of good lattice rules
Mathematics of Computation
Component-By-Component Construction of Good Intermediate-Rank Lattice Rules
SIAM Journal on Numerical Analysis
Weighted intermediate rank lattice rules with applications in finance
MOAS'07 Proceedings of the 18th conference on Proceedings of the 18th IASTED International Conference: modelling and simulation
Generating inverse Gaussian random variates by approximation
Computational Statistics & Data Analysis
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This paper discusses the intermediate rank lattice rule for the general case when the number of quadrature points is n^tm, where m is a composite integer, t is the rank of the rule, n is an integer such that (n,m)=1. By using the technique of averaging the quantity P"@a, we obtained a general expression for the average of P"@a over a subset of Z^s, derived an upper bound and the asymptotic rate for intermediate rank lattice rule. The results recover the cases of the conventional good lattice rule and the maximal rank rule. Computer search results show that P"2's by the intermediate rank lattice rules are smaller than those by good lattice rule, while searching intermediate rank lattice points is much faster than that of good lattice points for very close numbers of quadrature points. Numerical tests for application to an option pricing problem show that the intermediate rank lattice rules are not worse than the conventional good lattice rule on average. All the lattice rules show superiority over the Sobol' sequence, which beats the pseudo-random point sets.