An introduction to lattice rules and their generator matrices

IMA Journal of Numerical Analysis

Volumn 9, Issue 3, 1989, Pages 405-419

  Lyness, J N ^a  

^a ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037948473     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/9.3.405     Document Type: Article

References (17)

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5. Hua Loo Keng, & Wang Yuan 1981 Applications of Number Theory to Numerical Analysis. Berlin: Springer-Verlag.
6. Korobov, N. M. 1959 The approximate computation of multiple integrals (Russian). Dokl. Akad. Nauk. SSSR 124, 1207-1210.
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8. Lyness, J. N. 1988 Some comments on quadrature rule construction criteria. In: Numerical Integration III (G. Hämmerlin & H. Brass, Eds), ISNM voi. 85. Basel: Birkhäuser Verlag, 117-129.
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11. Sloan, I. H. 1985 Lattice methods for multiple integration. J. Comp. Appi. Math. 12,13, 131-143.
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13. Sloan, I. H., & Kachoyan, P. J. 1987 Lattice methods for multiple integration: theory, error analysis and examples. SIAM J. Numer. Anal. 24, 116-128.
14. Sloan, I. H., & Lyness, J. N. 1989 The representation of lattice quadrature rules as multiple sums. Math. Comp. 52, 81-94.
15. Sloan, I. H., & Walsh, L. 1988 Lattice rules - classification and searches. In: Numerical Integration IH (G. Hämmerlin and H. Brass, Eds), ISNM voi. 85. Birkhäuser Verlag,251-260.
16. Zaremba, S. K. 1966 Good lattice points, discrepancy and numerical integration. Ann. Mat. Pura Appl. 73, 293-317.
17. Zaremba, S. K. 1972 La méthode des “bons treillis” pour le calcul des intégrales multiples. In: Application of Number Theory to Numerical Analysis (S. K. Zaremba, Ed.) London: Academic Press, 39-119.