A search program for finding optimal integration lattices

DOI10.1007/BF02253429zbMath0749.65018OpenAlexW1542006974MaRDI QIDQ1180341

J. N. Lyness, Tor Sørevik

Publication date: 27 June 1992

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02253429

zbMATH Keywords

hypercubesearch algorithmlattice rulesperiodic functionsZaremba indexmultidimensional quadraturenumber theoretic rulesgood latticesoptimal integration latticessenior lattices

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Software, source code, etc. for problems pertaining to measure and integration (28-04)

Related Items (10)

The index of merit of \(k\)th-copy integration lattices ⋮ Ian Sloan and Lattice Rules ⋮ Lattice rules of minimal and maximal rank with good figures of merit ⋮ Lattice Rules by Component Scaling ⋮ An algorithm for finding optimal integration lattices of composite order ⋮ Determination of the rank of an integration lattice ⋮ Component-by-component construction of good lattice rules ⋮ Good low degree rank-1 lattice rules of high dimension ⋮ Five-dimensional $K$-optimal lattice rules ⋮ Multidimensional pseudo-spectral methods on lattice grids

Cites Work

• Tables of good lattices in four and five dimensions
• The number of lattice rules
• A table of good lattice points in three dimensions
• An Introduction to Lattice Rules and their Generator Matrices
• The Representation of Lattice Quadrature Rules as Multiple Sums
• Quasi-Monte Carlo methods and pseudo-random numbers
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