Quasi-Monte Carlo algorithms for unbounded, weighted integration problems

Journal of Complexity

Volumn 20, Issue 5, 2004, Pages 654-668

  Hartinger, Jürgen ^a   Kainhofer, Reinhold F ^a   Tichy, Robert F ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Non uniformly distributed low discrepancy sequences; Quasi Monte Carlo integration; Weighted integration

Indexed keywords

EID: 4444243396     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jco.2003.11.006     Document Type: Article

References (12)

1. P. Chelson, Quasi-random techniques for monte carlo methods, Ph.D. Dissertation, The Claremont Graduate School, 1976.
2. de Doncker E. Guan Y. Error bounds for the integration of singular functions using equidistributed sequences J. Complexity 19 2003 259-271
3. Devroye L. Nonuniform Random Variate Generation 1986 Springer New York
4. Drmota M. Tichy R. Sequences, Discrepancies and Applications Lecture Notes in Mathematics Vol. 1651 1997 Springer, New York, Berlin, Heidelberg, Tokyo
5. Hlawka E. Funktionen von beschränkter Variation in der Theorie der Gleichverteilung Ann. Mat. Pura Appl. 54 4 1961 325-333
6. Hlawka E. Gleichverteilung und Simulation Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 1997 183-216
7. E. Hlawka, R. Mück, A transformation of equidistributed sequences, in: Applications of Number Theory to Numerical Analysis, Academic Press, New York, 1972, pp. 371-388.
8. Hlawka E. Mück R. Über eine Transformation von gleichverteilten Folgen. II Computing 9 1972 127-138
9. Klinger B. Numerical integration of singular integrands using low-discrepancy sequences Computing 59 3 1997 223-236
10. Kuipers L. Niederreiter H. Uniform Distribution of Sequences 1974 Wiley-Interscience Publishers New York
11. Niederreiter H. Random number generation and quasi-Monte Carlo methods SIAM Conference Series in Applied Mathematics Vol. 63 1992 SIAM Philadelphia
12. Sobol′ I.M. Calculation of improper integrals using uniformly distributed sequences Soviet Math. Dokl. 14 3 1973 734-738