Efficient algorithms for computing the L2-discrepancy

Mathematics of Computation

Volumn 65, Issue 216, 1996, Pages 1621-1633

  Heinrich, S ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030500043     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-96-00756-9     Document Type: Article

References (17)

1. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, Reading, Massachusetts, 1974. MR 54:1706
2. V. A. Bykovskii. On the correct order of the error of optimal cubature formulas in spaces with dominant derivative, and on quadratic deviations of grids, Preprint, Computing Center Far-Eastern Scientific Center, Acad. Sci. USSR, Vladivostok, 1985. (Russian) [R. Zh. Mat. 1986, 7B 1663.]
3. H. Davenport, Note on irregularities of distribution, Mathematika, 3:131-135, 1956. MR 18:566a
4. D. Dobkin and D. Eppstein, Computing the discrepancy, Proceedings of the. Ninth Annual Symposium on Computational Geometry, pages 47-52, 1993.
5. D. Dobkin and D. Gunopulos, Computing the rectangle discrepancy. Preprint, Princeton University, 1994.
6. p-metric, 2 ≤ p < ∞, Dokl. Akad. Nauk SSSR, 252:805-807, 1980. English transl. in Soviet Math. Dokl. 21 (1980). MR 81k:10087
7. p-metric, 2 ≤ p < ∞, Dokl. Akad. Nauk SSSR, 252:805-807, 1980. English transl. in Soviet Math. Dokl. 21 (1980). MR 81k:10087
8. K. Mulmuley, Computational geometry. An introduction through randomized algorithms, Prentice Hall, Englewood Cliffs, New Jersey, 1994.
9. H. Niederreiter, Quasi-Monte Carlo methods and pseudo random numbers, Bull. Amer. Math. Soc., 84:957-1041, 1978.
10. H. Niederreiter, Random number generation and quasi-Monte Carlo methods, SIAM, Philadelphia, 1992. MR 93h:65008
11. S. H. Paskov, Average case complexity of multivariate integratic n for smooth functions, J. Complexity, 9:291-312, 1993. MR 94f:65135
12. K. F. Roth, On irregularities of distribution, Mathematika, 1:73-79, 1954. MR 16:575c
13. K. F. Roth, On irregularities of distribution, IV, Acta Arith., 37:67-75, 1980. MR 82f:10063
14. V. N. Temlyakov, On a way of obtaining lower estimates for the errors of quadrature formulas, Mat. Sbornik, 181:1403-1413, 1990. English transl.: Math. USSR Sbornik, 71, (1992), pp. 247-257. MR 92a:65083
15. V. N. Temlyakov, On a way of obtaining lower estimates for the errors of quadrature formulas, Mat. Sbornik, 181:1403-1413, 1990. English transl.: Math. USSR Sbornik, 71, (1992), pp. 247-257. MR 92a:65083
16. T. T. Warnock, Computational investigations of low discrepancy point sets. In S. K. Zaremba, editor, Applications of Number Theory to Numerical Analysis, Academic Press, New York, 1972, pp. 319-343. MR 50:3526
17. H. Woźniakowski, Average case complexity of multivariate integration, Bull. Amer. Math. Soc., 24:185-194, 1991. MR 91i:65224