메뉴 건너뛰기




Volumn 13, Issue 4, 2003, Pages 363-378

Variance with alternative scramblings of digital nets

Author keywords

Derandomization; Quasi Monte Carlo; Randomization

Indexed keywords

DERANDOMIZATION; QUASI-MONTE CARLO; RANDOMIZATION; SCRAMBLING METHODS;

EID: 4243059534     PISSN: 10493301     EISSN: None     Source Type: Journal    
DOI: 10.1145/945511.945518     Document Type: Article
Times cited : (88)

References (38)
  • 3
    • 0000272653 scopus 로고
    • Randomization of number theoretic methods for multiple integration
    • CRANLEY, R. AND PATTERSON, T. 1976. Randomization of number theoretic methods for multiple integration. SIAM J. Numer. Anal. 13, 904-914.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 904-914
    • Cranley, R.1    Patterson, T.2
  • 5
    • 0001013260 scopus 로고
    • Discrepance de suites associées à un système de numération (en dimension s)
    • FAURE, H. 1982. Discrepance de suites associées à un système de numération (en dimension s). Acta Arithmet. 41, 337-351.
    • (1982) Acta Arithmet. , vol.41 , pp. 337-351
    • Faure, H.1
  • 6
    • 40649093267 scopus 로고
    • Good permutations for extreme discrepancy
    • FAURE, H. 1992. Good permutations for extreme discrepancy. J. Numb. Theory 42, 47-56.
    • (1992) J. Numb. Theory , vol.42 , pp. 47-56
    • Faure, H.1
  • 7
    • 0035704436 scopus 로고    scopus 로고
    • Variations on (0,s)-sequences
    • FAURE, H. 2001. Variations on (0,s)-sequences. J. Complex. 17, 741-753.
    • (2001) J. Complex. , vol.17 , pp. 741-753
    • Faure, H.1
  • 8
    • 0008854038 scopus 로고    scopus 로고
    • Another random scrambling of digital (t,s)-sequences
    • K. T. Fang, F. J. Hickernell, and H. Niederreiter, Eds. Springer-Verlag, Berlin, Germany
    • FAURE, H. AND TEZUKA, S. 2002. Another random scrambling of digital (t,s)-sequences. In Monte Carlo and Quasi-Monte Carlo Methods 2000, K. T. Fang, F. J. Hickernell, and H. Niederreiter, Eds. Springer-Verlag, Berlin, Germany, 242-256.
    • (2002) Monte Carlo and Quasi-Monte Carlo Methods 2000 , pp. 242-256
    • Faure, H.1    Tezuka, S.2
  • 10
    • 0003378660 scopus 로고    scopus 로고
    • Fast generation of randomized low-discrepancy point sets
    • K. T. Fang, F. J. Hickernell, and H. Niederreiter, Eds. Springer-Verlag, Berlin, Germany
    • FRIEDEL, I. AND KELLER, A. 2002. Fast generation of randomized low-discrepancy point sets. In Monte Carlo and Quasi-Monte Carlo Methods 2000, K. T. Fang, F. J. Hickernell, and H. Niederreiter, Eds. Springer-Verlag, Berlin, Germany, 257-273.
    • (2002) Monte Carlo and Quasi-Monte Carlo Methods 2000 , pp. 257-273
    • Friedel, I.1    Keller, A.2
  • 11
    • 0347798660 scopus 로고
    • A modified Monte Carlo quadrature, II
    • HABER, S. 1967. A modified Monte Carlo quadrature, II. Math. Computat. 21, 388-397.
    • (1967) Math. Computat. , vol.21 , pp. 388-397
    • Haber, S.1
  • 12
    • 0001015105 scopus 로고
    • Random approximation in numerical analysis
    • (Essen, Germany, Nov. 24-30). K. D. Bierstedt, A. Pietsch, W. M. Ruess, and D. Vogt, Eds. Marcel Dekker, New York
    • HEINRICH, S. 1993. Random approximation in numerical analysis. In Functional analysis. Proceedings of the Essen Conference (Essen, Germany, Nov. 24-30). K. D. Bierstedt, A. Pietsch, W. M. Ruess, and D. Vogt, Eds. Marcel Dekker, New York, 123-171.
    • (1993) Functional Analysis. Proceedings of the Essen Conference , pp. 123-171
    • Heinrich, S.1
  • 13
    • 0030259017 scopus 로고    scopus 로고
    • The mean square discrepancy of randomized nets
    • HICKERNELL, F. J. 1996a. The mean square discrepancy of randomized nets. ACM Trans. Model. Comput. Simul. 6, 274-296.
    • (1996) ACM Trans. Model. Comput. Simul. , vol.6 , pp. 274-296
    • Hickernell, F.J.1
  • 14
    • 0000790253 scopus 로고    scopus 로고
    • Quadrature error bounds and figures of merit for quasi-random points
    • HICKERKELL, F. J. 1996b. Quadrature error bounds and figures of merit for quasi-random points. SIAM J. Numer. Anal. 33, 1995-2016. Corrected printing of Sections 3-6 in ibid., 34 (1997), 853-866.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1995-2016
    • Hickerkell, F.J.1
  • 15
    • 0037538298 scopus 로고    scopus 로고
    • HICKERKELL, F. J. 1996b. Quadrature error bounds and figures of merit for quasi-random points. SIAM J. Numer. Anal. 33, 1995-2016. Corrected printing of Sections 3-6 in ibid., 34 (1997), 853-866.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 853-866
  • 16
    • 0032345316 scopus 로고    scopus 로고
    • A generalized discrepancy and quadrature error bound
    • HICKERNELL, F. J. 1998a. A generalized discrepancy and quadrature error bound. Math. Comput. 67, 299-322.
    • (1998) Math. Comput. , vol.67 , pp. 299-322
    • Hickernell, F.J.1
  • 17
    • 0001297776 scopus 로고    scopus 로고
    • Lattice rules: How well do they measure up?
    • P. Hellekalek and G. Larcher, Eds. Springer, New York
    • HICKERNELL, F. J. 1998b. Lattice rules: how well do they measure up? In Random and Quasi-Random Point Sets, P. Hellekalek and G. Larcher, Eds. Springer, New York, 109-168.
    • (1998) Random and Quasi-Random Point Sets , pp. 109-168
    • Hickernell, F.J.1
  • 18
    • 0034432296 scopus 로고    scopus 로고
    • The mean square discrepancy of scrambled (t, s)-sequences
    • HICKERNELL, F. J. AND YUE, R. X. 2000. The mean square discrepancy of scrambled (t, s)-sequences. SIAM J. Numer. Anal. 38, 1089-1112.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1089-1112
    • Hickernell, F.J.1    Yue, R.X.2
  • 19
    • 0000489595 scopus 로고
    • Funktionen von beschränkter Variation in der Theorie der Gleichverteilung
    • HLAWKA, E. 1961. Funktionen von beschränkter Variation in der Theorie der Gleichverteilung. Ann. Mate. Pura Appl. 54, 325-333.
    • (1961) Ann. Mate. Pura Appl. , vol.54 , pp. 325-333
    • Hlawka, E.1
  • 20
    • 0038934825 scopus 로고    scopus 로고
    • The asymptotic efficiency of randomized nets for quadrature
    • HONG, H. S. AND HICKERNELL, F. J. 1999. The asymptotic efficiency of randomized nets for quadrature. Math. Comput. 68, 767-791.
    • (1999) Math. Comput. , vol.68 , pp. 767-791
    • Hong, H.S.1    Hickernell, F.J.2
  • 21
  • 22
    • 0002922737 scopus 로고    scopus 로고
    • A survey of randomized quasi-Monte Carlo methods
    • M. Dror, P. L'Ecuyer, and F. Szidarovszki, Eds. Kluwer Academic Publishers, New York
    • L'ECUYER, P. AND LEMIEUX, C. 2002. A survey of randomized quasi-Monte Carlo methods. In Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, M. Dror, P. L'Ecuyer, and F. Szidarovszki, Eds. Kluwer Academic Publishers, New York, 419-474.
    • (2002) Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications , pp. 419-474
    • L'Ecuyer, P.1    Lemieux, C.2
  • 24
    • 0000382131 scopus 로고    scopus 로고
    • 2-discrepancy for anchored boxes
    • 2-discrepancy for anchored boxes. J. Complex. 14, 527-556.
    • (1998) J. Complex. , vol.14 , pp. 527-556
    • Matoušek, J.1
  • 26
    • 0001491057 scopus 로고
    • Randomly permuted (t, m, s)-nets and (t, s)-sequences
    • H. Niederreiter and P. J.-S. Shiue, Eds. Springer-Verlag, New York
    • OWEN, A. B. 1995. Randomly permuted (t, m, s)-nets and (t, s)-sequences. In Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J.-S. Shiue, Eds. Springer-Verlag, New York, 299-317.
    • (1995) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing , pp. 299-317
    • Owen, A.B.1
  • 27
    • 0013036522 scopus 로고    scopus 로고
    • Monte Carlo variance of scrambled equidistribution quadrature
    • OWEN, A. B. 1997a. Monte Carlo variance of scrambled equidistribution quadrature. SIAM J. Numer. Anal. 34, 5, 1884-1910.
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.5 , pp. 1884-1910
    • Owen, A.B.1
  • 28
    • 0031509503 scopus 로고    scopus 로고
    • Scrambled net variance for integrals of smooth functions
    • OWEN, A. B. 1997b. Scrambled net variance for integrals of smooth functions. Ann. Stat. 25, 4, 1541-1562.
    • (1997) Ann. Stat. , vol.25 , Issue.4 , pp. 1541-1562
    • Owen, A.B.1
  • 29
    • 0031599238 scopus 로고    scopus 로고
    • Latin supercube sampling for very high dimensional simulations
    • OWEN, A. B. 1998. Latin supercube sampling for very high dimensional simulations. ACM Trans. Model. Comput. Simul. 8, 2, 71-102.
    • (1998) ACM Trans. Model. Comput. Simul. , vol.8 , Issue.2 , pp. 71-102
    • Owen, A.B.1
  • 30
    • 0008846507 scopus 로고    scopus 로고
    • Monte Carlo, quasi-Monte Carlo, and randomized quasi-Monte Carlo
    • H. Niederreiter and J. Spanier, Eds, Springer-Verlag, Berlin
    • OWEN, A. B. 1999. Monte Carlo, quasi-Monte Carlo, and randomized quasi-Monte Carlo. In Monte Carlo and quasi-Monte Carlo Methods 1998, H. Niederreiter and J. Spanier, Eds, Springer-Verlag, Berlin, 86-97.
    • (1999) Monte Carlo and Quasi-Monte Carlo Methods 1998 , pp. 86-97
    • Owen, A.B.1
  • 31
    • 37949004450 scopus 로고
    • On irregularities of distribution IV
    • ROTH, K. F. 1980. On irregularities of distribution IV. Acta Arithmet. 37, 67-75.
    • (1980) Acta Arithmet. , vol.37 , pp. 67-75
    • Roth, K.F.1
  • 32
    • 0346930427 scopus 로고    scopus 로고
    • Applications of randomized low discrepancy sequences to the valuation of complex securities
    • TAN, K. S. AND BOYLE, P. P. 2000. Applications of randomized low discrepancy sequences to the valuation of complex securities, J. Econ. Dynam. Cont. 24, 1747-1782.
    • (2000) J. Econ. Dynam. Cont. , vol.24 , pp. 1747-1782
    • Tan, K.S.1    Boyle, P.P.2
  • 34
    • 4243134372 scopus 로고    scopus 로고
    • On randomization of generalized faure sequences
    • IBM Tokyo Research Laboratory
    • TEZUKA, S. 2002. On randomization of generalized faure sequences. Tech. Rep. RT0494, IBM Tokyo Research Laboratory.
    • (2002) Tech. Rep. , vol.RT0494
    • Tezuka, S.1
  • 35
    • 4243159241 scopus 로고    scopus 로고
    • I-binomial scrambling of digital nets and sequences
    • IBM Tokyo Research Laboratory
    • TEZUKA, S. AND FAURE, H. 2002. I-binomial scrambling of digital nets and sequences. Tech. Rep., IBM Tokyo Research Laboratory.
    • (2002) Tech. Rep.
    • Tezuka, S.1    Faure, H.2
  • 38
    • 0002548979 scopus 로고
    • Some applications of multidimensional integration by parts
    • ZAREMBA, S. K. 1968. Some applications of multidimensional integration by parts. Ann. Pol. Math. 21, 85-96.
    • (1968) Ann. Pol. Math. , vol.21 , pp. 85-96
    • Zaremba, S.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.