Different quality indexes for lattice rules
This paper is concerned with methods for comparing lattice rules for the numerical computation of multiple integrals. Lattice rules are exact for certain sets of trigonometric polynomials, and roughly speaking, the quality of a lattice rule depends on how efficient the rule is at exactly integrating classes of trigonometric monomials. The authors define hyperbolic, hexagonal, spherical and octahedral quality indices for lattice rules and prove extremal properties for these indices. The paper then focuses on two-dimensional rules. Some new rules are presented that form a minimal family of the octahedral index. The hyperbolic, hexagonal and spherical quality indices for the new rules are derived and compared with the spherical index for some rules whose generators depend on the convergents of a continued fraction.
scientific article; zbMATH DE number 1069067
scientific article