메뉴 건너뛰기




Volumn 33, Issue 5, 1996, Pages 1995-2016

Quadrature error bounds with applications to lattice rules

Author keywords

ANOVA decomposition; Good lattice points; Imbedded rules; Monte Carlo; Multidimensional integration; Number theoretic; Periodic functions; Quasirandom; Reproducing kernel Hilbert spaces

Indexed keywords


EID: 0000790253     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994261439     Document Type: Article
Times cited : (57)

References (28)
  • 2
    • 5844297152 scopus 로고
    • Theory of reproducing kernels
    • M. ARONSZAJN, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), pp. 337-404.
    • (1950) Trans. Amer. Math. Soc. , vol.68 , pp. 337-404
    • Aronszajn, M.1
  • 3
    • 84966232258 scopus 로고
    • Error bounds for the method of good lattice points
    • S. DISNEY AND I. H. SLOAN, Error bounds for the method of good lattice points, Math. Comp., 56 (1991), pp. 257-266.
    • (1991) Math. Comp. , vol.56 , pp. 257-266
    • Disney, S.1    Sloan, I.H.2
  • 4
    • 0026841788 scopus 로고
    • Lattice integration rules of maximal rank formed by copying rank 1 rules
    • _, Lattice integration rules of maximal rank formed by copying rank 1 rules, SIAM J. Numer. Anal., 29 (1992), pp. 566-577.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 566-577
  • 5
    • 0001368656 scopus 로고
    • The jackknife estimate of variance
    • B. EFRON AND C. STEIN, The jackknife estimate of variance, Ann. Statist., 9 (1981), pp. 586-596.
    • (1981) Ann. Statist. , vol.9 , pp. 586-596
    • Efron, B.1    Stein, C.2
  • 7
    • 0013448247 scopus 로고
    • Testing multidimensional integration routines
    • B. Ford, J. C. Rault, and F. Thomasset, eds., North-Holland, Amsterdam
    • A. GENZ, Testing multidimensional integration routines, in Tools, Methods and Languages for Scientific and Engineering Computation, B. Ford, J. C. Rault, and F. Thomasset, eds., North-Holland, Amsterdam, 1984, pp. 81-94.
    • (1984) Tools, Methods and Languages for Scientific and Engineering Computation , pp. 81-94
    • Genz, A.1
  • 8
    • 0040457640 scopus 로고
    • A package for testing multiple integration subroutines
    • P. Keast and G. Fairweather, eds., Dordrecht, the Netherlands, D. Reidel
    • _, A package for testing multiple integration subroutines, in Numerical Integration: Recent Developments, Software and Applications, P. Keast and G. Fairweather, eds., Dordrecht, the Netherlands, D. Reidel, 1987, pp. 337-340.
    • (1987) Numerical Integration: Recent Developments, Software and Applications , pp. 337-340
  • 9
    • 0039044603 scopus 로고
    • A comparison of random and quasirandom points for multidimensional quadrature
    • Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J.-S. Shiue, eds., Springer-Verlag, Berlin
    • F. J. HICKERNELL, A comparison of random and quasirandom points for multidimensional quadrature, in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J.-S. Shiue, eds., Lecture Notes in Statistics, Vol. 106, Springer-Verlag, Berlin, 1995, pp. 213-227.
    • (1995) Lecture Notes in Statistics , vol.106 , pp. 213-227
    • Hickernell, F.J.1
  • 10
    • 0038285786 scopus 로고
    • Zur angenäherten berechnung mehrfacher integrale
    • E. HLAWKA, Zur angenäherten berechnung mehrfacher integrale, Monatsh. Math., 66 (1962), pp. 140-151.
    • (1962) Monatsh. Math. , vol.66 , pp. 140-151
    • Hlawka, E.1
  • 12
    • 0027576527 scopus 로고
    • Intermediate rank lattice rules for multidimensional integration
    • S. JOE AND S. A. R. DISNEY, Intermediate rank lattice rules for multidimensional integration. SIAM J. Numer. Anal., 30 (1993), pp. 569-582.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 569-582
    • Joe, S.1    Disney, S.A.R.2
  • 13
    • 0026909088 scopus 로고
    • Imbedded lattice rules for multidimensional integration
    • S. JOE AND I. H. SLOAN, Imbedded lattice rules for multidimensional integration, SIAM J. Numer. Anal., 29 (1992), pp. 1119-1135.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1119-1135
    • Joe, S.1    Sloan, I.H.2
  • 14
    • 0001347330 scopus 로고
    • The approximate computation of multiple integrals
    • In Russian
    • N. M. KOROBOV, The approximate computation of multiple integrals. Dokl. Akad. Nauk. UzSSR. 124 (1959), pp. 1207-1210. (In Russian.)
    • (1959) Dokl. Akad. Nauk. UzSSR , vol.124 , pp. 1207-1210
    • Korobov, N.M.1
  • 15
    • 0001563525 scopus 로고
    • Quasi-random sequences and their discrepancies
    • W. J. MOROKOFF AND R. E. CAFLISCH, Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput., 15 (1994), pp. 1251-1279.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1251-1279
    • Morokoff, W.J.1    Caflisch, R.E.2
  • 17
    • 84966204166 scopus 로고
    • Lattice rules for multiple integration and discrepancy
    • H. NIEDERREITER AND I. H. SLOAN, Lattice rules for multiple integration and discrepancy, Math. Comp., 54 (1990), pp. 303-312.
    • (1990) Math. Comp. , vol.54 , pp. 303-312
    • Niederreiter, H.1    Sloan, I.H.2
  • 18
    • 0040457620 scopus 로고
    • Quasi-Monte Carlo methods with modified vertex weights
    • Birkhäuser, Basel
    • _, Quasi-Monte Carlo methods with modified vertex weights, in Numerical Integration IV, Internat. Series Numerical Math., Vol. 112, Birkhäuser, Basel, 1993, pp. 253-265.
    • (1993) Numerical Integration IV, Internat. Series Numerical Math. , vol.112 , pp. 253-265
  • 19
    • 0028430051 scopus 로고
    • Integration of nonperiodic functions of two variables by Fibonacci lattice rules
    • _, Integration of nonperiodic functions of two variables by Fibonacci lattice rules, J. Comput. Appl. Math., 51 (1994). pp. 57-70.
    • (1994) J. Comput. Appl. Math. , vol.51 , pp. 57-70
  • 20
    • 0000444881 scopus 로고
    • Orthogonal arrays for computer experiments, integration and visualization
    • A. B. OWEN, Orthogonal arrays for computer experiments, integration and visualization, Statist. Sinica, 2 (1992), pp. 439-452.
    • (1992) Statist. Sinica , vol.2 , pp. 439-452
    • Owen, A.B.1
  • 22
    • 0004791021 scopus 로고
    • Lattice methods for multiple integration
    • I. H. SLOAN, Lattice methods for multiple integration, J. Comput. Appl. Math., 12 & 13 (1985), pp. 131-143.
    • (1985) J. Comput. Appl. Math. , vol.12-13 , pp. 131-143
    • Sloan, I.H.1
  • 23
    • 0042435988 scopus 로고
    • Numerical integration in high dimensions - The lattice rule approach
    • T. O. Espelid and A. Genz, eds., Kluwer Academic Publishers, Dordrecht
    • _, Numerical integration in high dimensions - the lattice rule approach, in Numerical Integration: Recent Developments, Software and Applications, T. O. Espelid and A. Genz, eds., Kluwer Academic Publishers, Dordrecht, 1992, pp. 55-69.
    • (1992) Numerical Integration: Recent Developments, Software and Applications , pp. 55-69
  • 25
    • 0023289278 scopus 로고
    • Lattice methods for multiple integration: Theory, error analysis and examples
    • I. H. SLOAN AND P. KACHOYAN, Lattice methods for multiple integration: Theory, error analysis and examples, SIAM J. Numer. Anal., 24 (1987), pp. 116-128.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 116-128
    • Sloan, I.H.1    Kachoyan, P.2
  • 26
    • 84966216940 scopus 로고
    • A computer search of rank-2 lattice rules for multidimensional quadrature
    • I. H. SLOAN AND L. WALSH, A computer search of rank-2 lattice rules for multidimensional quadrature, Math. Comp., 54 (1990), pp. 281-302.
    • (1990) Math. Comp. , vol.54 , pp. 281-302
    • Sloan, I.H.1    Walsh, L.2
  • 27
    • 0003466536 scopus 로고
    • Society for Industrial and Applied Mathematics, Philadelphia
    • G. WAHBA, Spline Models for Observational Data, Society for Industrial and Applied Mathematics, Philadelphia, 1990.
    • (1990) Spline Models for Observational Data
    • Wahba, G.1
  • 28
    • 0002239882 scopus 로고
    • Computational investigtions of low discrepancy point sets
    • S. K. Zaremba, ed., Academic Press. New York
    • T. T. WARNOCK, Computational investigtions of low discrepancy point sets, in Applications of Number Theory to Numerical Analysis, S. K. Zaremba, ed., Academic Press. New York, 1972, pp. 319-343.
    • (1972) Applications of Number Theory to Numerical Analysis , pp. 319-343
    • Warnock, T.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.