Quasi-random integration in high dimensions

Mathematics and Computers in Simulation

Volumn 73, Issue 5, 2007, Pages 309-319

  Takhtamyshev, George ^a   Vandewoestyne, Bart ^b   Cools, Ronald ^b  

^a KULeuven ^*  (United States)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Cubature; Multivariate numerical integration; Quasi Monte Carlo

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FUNCTIONS; MATHEMATICAL MODELS; MONTE CARLO METHODS; MULTIVARIABLE CONTROL SYSTEMS; PARAMETER ESTIMATION;

CUBATURE; MULTIVARIATE NUMERICAL INTEGRATION; QUASI-MONTE CARLO; RICHTMYER SEQUENCES;

INTEGRATION;

EID: 33845571436     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2006.04.001     Document Type: Article

References (21)

1. τ-sequences. USSR Comput. Math. Math. Phys. 19 (1979) 252-256
2. Bratley P., and Fox B.L. Algorithm 659: implementing Sobol's quasirandom sequence generator. ACM Trans. Math. Software 14 1 (March) (1988) 88-100
3. E.M. da Silva, T. Barbe, Quasi Monte Carlo in Finance: Extending for High Dimensional Problems, May 2003.
4. A. Genz, Testing multidimensional integration routines, in: B. Ford, J.C. Rault, F. Thomasset (Eds.), Tools, Methods and Languages for Scientific and Engineering Computation, INRIA, Elsevier North-Holland, Inc., Paris, France, 1984.
5. Holian B.L., Percus O.E., Warnock T.T., and Whitlock P.A. Pseudorandom number generator for massively parallel molecular-dynamics simulations. Phys. Rev. E 50 2 (August) (1994) 1607-1615
6. Jäckel P. Monte Carlo Methods in Finance (2002), J. Wiley & Sons Ltd, Baffins Lane, Chichester, England
7. James F., Hoogland J., and Kleiss R. Multidimensional sampling for simulation and integration: measures, discrepancies and quasi-random numbers. Comput. Phys. Commun. 99 2 (1997) 180-220
8. Joe S., and Kuo F.Y. Remark on algorithm 659: implementing Sobol's quasirandom sequence generator. ACM Trans. Math. Software 29 1 (March 2003) 49-57
9. L'Ecuyer P. Efficient and portable combined random number generators. Commun. ACM 31 (1988) 742-749
10. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, vol. 63 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1992.
11. Park S.K., and Miller K.W. Random number generators: good ones are hard to find. Commun. ACM 31 10 (October) (1988) 1192-1201
12. Percus O.E., and Whitlock P.A. Theory and application of Marsaglia's monkey test for pseudorandom number generators. ACM Trans. Model. Comput. Simul. 5 2 (April 1995) 87-100
13. Press W.H., and Teukolsky S.A. Quasi- (that is, sub-) random numbers. Comput. Phys. 3 November-December (1989) 76-79
14. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes in Fortran 77. second ed. (1992), Cambridge University Press
15. Schlier Ch. Discrepancy behavior in the non-asymptotic regime. Appl. Numer. Math. 50 (2004) 227-238
16. Schlier Ch. Error trends in quasi-Monte Carlo integration. Comput. Phys. Commun. 159 (2004) 93-105
17. Sobol' I.M. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7 (1967) 86-112
18. Sobol' I.M. On the systematic search in a hypercube. SIAM J. Numer. Anal. 16 5 (October) (1979) 790-793
19. Sobol' I.M., and Asotsky D.I. One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods. Math. Comput. Simul. 62 3-6 (March 2003) 255-263
20. Sobol' I.M. Uniformly distributed sequences with an additional uniform property. USSR Comput. Math. Math. Phys. 16 (1976) 236-242
21. H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins. Mathematische Annalen 77 (1916) 313-352.