A useful result in searches for good vertex-modified number-theoretic rules
This paper is concerned with how to efficiently search for good parameters for certain types of lattice rules for the numerical computation of multiple integrals. The work is based on a theorem of Korobov that can be used to restrict the search domain for lattice rules. The original theorem appeared in a Russian book and had not been widely known. It was rediscovered by the author, who provides a short proof. The theorem is applied to searches for the vertex-modified lattice rules that are useful for the integration of non-periodic functions. Searches to minimize quadratic discrepancy and searches to minimize vertex variance are both considered. In each case, it is shown that the application of the theorem can reduce the search time by a factor of approximately two.
scientific article; zbMATH DE number 932493
scientific article