Three- and four-dimensional 𝐾-optimal lattice rules of moderate trigonometric degree

DOI10.1090/S0025-5718-01-01326-6zbMath0985.41020OpenAlexW2076760134WikidataQ57779042 ScholiaQ57779042MaRDI QIDQ2723528

J. N. Lyness, Ronald Cools

Publication date: 5 July 2001

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01326-6

zbMATH Keywords

cubature ruleslattaice rulesoptimal rules

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Exponential convergence and tractability of multivariate integration for Korobov spaces, Five- and six-dimensional lattice rules generated by structured matrices, The index of merit of \(k\)th-copy integration lattices, Constructing lattice rules based on weighted degree of exactness and worst case error, Extremal lattices and the construction of lattice rules, Notes on lattice rules, Determination of the rank of an integration lattice, Good low degree rank-1 lattice rules of high dimension, Four-dimensional lattice rules generated by skew-circulant matrices, The Hermite normal form for certain rank-1 circulant and skew-circulant lattice rules, Five-dimensional $K$-optimal lattice rules, Multidimensional pseudo-spectral methods on lattice grids, On Error Estimates in Sp for Cubature Formulas Exact for Haar Polynomials, Discrepancy Theory and Quasi-Monte Carlo Integration

Cites Work

• Smolyak's construction of cubature formulas of arbitrary trigonometric degree
• Different quality indexes for lattice rules
• An Introduction to Lattice Rules and their Generator Matrices
• Lattice Rules by Component Scaling
• Cubature Rules of Prescribed Merit
• Minimal cubature formulae of trigonometric degree
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