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Different Quality Indexes for Lattice Rules |
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| Institution: | 1. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200 A, B-3001, Heverlee, Belgium;2. Department of Industrial and Applied Mathematics, Division of Science & Technology, Tamaki Campus, The University of Auckland, Private Bag 92019, Auckland, New Zealand |
| Abstract: | We consider lattice rules (i.e. cubature formulas with equal coefficients whose nodes lie on a lattice) which are exact for trigonometric polynomials in two variables with different spectra. Various quality indexes are characterized. Extremal properties of indexes are obtained. A new family of lattice rules of trigonometric degree is presented. Also a family of lattice rules exact on trigonometric polynomials of a hexagonal spectrum is constructed. |
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