The Representation of Lattice Quadrature Rules as Multiple Sums

DOI10.2307/2008654zbMath0659.65018OpenAlexW4240803397MaRDI QIDQ3809113

J. N. Lyness, Ian H. Sloan

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2008654

zbMATH Keywords

numerical quadraturelattice rulescubature formulasproduct trapezoidal rulenumber-theoretic rules

Mathematics Subject Classification ID

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

Related Items (22)

Integration of nonperiodic functions of two variables by Fibonacci lattice rules ⋮ The existence of efficient lattice rules for multidimensional numerical integration ⋮ The determination of canonical forms for lattice quadrature rules ⋮ The number of lattice rules having given invariants ⋮ A generative classification of mesh refinement rules with lattice transformations ⋮ Ian Sloan and Lattice Rules ⋮ Integral Equations, Quasi-Monte Carlo Methods and Risk Modeling ⋮ Randomization of lattice rules for numerical multiple integration ⋮ Triangular canonical forms for lattice rules of prime-power order ⋮ Lattice rules of minimal and maximal rank with good figures of merit ⋮ On 2D packings of cubes in the torus ⋮ A search program for finding optimal integration lattices ⋮ Lattice Rules by Component Scaling ⋮ The Existence of Efficient Lattice Rules for Multidimensional Numerical Integration ⋮ An algorithm for finding optimal integration lattices of composite order ⋮ Determination of the rank of an integration lattice ⋮ Moment discretization for ill-posed problems with discrete weakly bounded noise ⋮ A Generalized Sampling Theorem for Locally Compact Abelian Groups ⋮ Lattice Rules: Projection Regularity and Unique Representations ⋮ The ultratriangular form for prime-power lattice rules ⋮ Minimal cubature formulae of trigonometric degree ⋮ On integration lattices

Cites Work

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• Zur angenäherten Berechnung mehrfacher Integrale
• Lattice methods for multiple integration
• Lattice Methods for Multiple Integration: Theory, Error Analysis and Examples
• Applications of Number Theory to Numerical Analysis
• Randomization of Number Theoretic Methods for Multiple Integration
• Quasi-Monte Carlo methods and pseudo-random numbers
• Optimal Parameters for Multidimensional Integration

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