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Volumn 20, Issue 4, 2004, Pages 493-522

On the convergence rate of the component-by-component construction of good lattice rules

Author keywords

Lattice rules; Numerical integration; Quasi Monte Carlo

Indexed keywords


EID: 3242738676     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jco.2003.11.008     Document Type: Article
Times cited : (68)

References (19)
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    • Reducing the construction cost of the component-by-component construction of good lattice rules
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    • J. Dick, F.Y. Kuo, Reducing the construction cost of the component-by-component construction of good lattice rules, Math. Comp. (2004), to appear
    • (2004) Math. Comp.
    • Dick, J.1    Kuo, F.Y.2
  • 3
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    • Inequalities
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    • (1934)
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  • 5
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    • Lattice rules: How well do they measure up?
    • P. Hellekalek, G. Larcher (Eds.), Berlin, New York: Springer
    • Hickernell F.J. Lattice rules: How well do they measure up? In: Hellekalek P. Larcher G. (Eds.). Random and Quasi-Random Point Sets 1998 109-166 Springer Berlin, New York
    • (1998) Random and Quasi-Random Point Sets , pp. 109-166
    • Hickernell, F.J.1
  • 6
    • 0041638501 scopus 로고    scopus 로고
    • Integration and approximation in arbitrary dimensions
    • Hickernell F.J. Woźniakowski H. Integration and approximation in arbitrary dimensions Adv. Comput. Math. 12 2000 25-58
    • (2000) Adv. Comput. Math. , vol.12 , pp. 25-58
    • Hickernell, F.J.1    Woźniakowski, H.2
  • 7
    • 0001347330 scopus 로고
    • The approximate computation of multiple integrals
    • (in Russian)
    • Korobov N.M. The approximate computation of multiple integrals Dokl. Akad. Nauk. SSSR 124 959 1207-1210 (in Russian)
    • (1959) Dokl. Akad. Nauk. SSSR , vol.124 , pp. 1207-1210
    • Korobov, N.M.1
  • 9
    • 0038392447 scopus 로고    scopus 로고
    • Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
    • Kuo F.Y. Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces J. Complexity 19 2003 301-320
    • (2003) J. Complexity , vol.19 , pp. 301-320
    • Kuo, F.Y.1
  • 10
    • 0036889417 scopus 로고    scopus 로고
    • Component-by-component construction of good lattice rules with a composite number of points
    • Kuo F.Y. Joe S. Component-by-component construction of good lattice rules with a composite number of points J. Complexity 18 2002 943-976
    • (2002) J. Complexity , vol.18 , pp. 943-976
    • Kuo, F.Y.1    Joe, S.2
  • 13
    • 0038624700 scopus 로고    scopus 로고
    • Constructing randomly shifted lattice rules in weighted Sobolev spaces
    • Sloan I.H. Kuo F.Y. Joe S. Constructing randomly shifted lattice rules in weighted Sobolev spaces SIAM J. Numer. Anal. 40 2002 1650-1665
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1650-1665
    • Sloan, I.H.1    Kuo, F.Y.2    Joe, S.3
  • 14
    • 0036790313 scopus 로고    scopus 로고
    • On the step-by-step construction of quasi-Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces
    • Sloan I.H. Kuo F.Y. Joe S. On the step-by-step construction of quasi-Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces Math. Comp. 71 2002 1609-1640
    • (2002) Math. Comp. , vol.71 , pp. 1609-1640
    • Sloan, I.H.1    Kuo, F.Y.2    Joe, S.3
  • 15
    • 0036003407 scopus 로고    scopus 로고
    • Component-by-component construction of good lattice rules
    • Sloan I.H. Reztsov A.V. Component-by-component construction of good lattice rules Math. Comp. 71 2002 263-273
    • (2002) Math. Comp. , vol.71 , pp. 263-273
    • Sloan, I.H.1    Reztsov, A.V.2
  • 17
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    • When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
    • Sloan I.H. Woźniakowski H. When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complexity 14 1998 1-33
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    • Sloan, I.H.1    Woźniakowski, H.2
  • 18
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    • Tractability of multivariate integration for weighted Korobov classes
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  • 19
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    • On Korobov lattice rules in weighted Korobov spaces
    • to appear
    • X. Wang, I.H. Sloan, J. Dick, On Korobov lattice rules in weighted Korobov spaces, SIAM J. Num. Anal. (2004), to appear
    • (2004) SIAM J. Num. Anal.
    • Wang, X.1    Sloan, I.H.2    Dick, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.