Points sets with low L p discrepancy

Peter Kritzer; Friedrich Pillichshammer

Mathematica Slovaca (2007)

  • Volume: 57, Issue: 1, page 11-32
  • ISSN: 0232-0525

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Kritzer, Peter, and Pillichshammer, Friedrich. "Points sets with low $L_p$ discrepancy." Mathematica Slovaca 57.1 (2007): 11-32. <http://eudml.org/doc/34630>.

@article{Kritzer2007,
author = {Kritzer, Peter, Pillichshammer, Friedrich},
journal = {Mathematica Slovaca},
keywords = {low discrepancy sequence; -discrepancy; Hammersley point sets; Hammersley sequence; digital shift},
language = {eng},
number = {1},
pages = {11-32},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Points sets with low $L_p$ discrepancy},
url = {http://eudml.org/doc/34630},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Kritzer, Peter
AU - Pillichshammer, Friedrich
TI - Points sets with low $L_p$ discrepancy
JO - Mathematica Slovaca
PY - 2007
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 57
IS - 1
SP - 11
EP - 32
LA - eng
KW - low discrepancy sequence; -discrepancy; Hammersley point sets; Hammersley sequence; digital shift
UR - http://eudml.org/doc/34630
ER -

References

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  1. BECK J.-CHEN W. W. L., Irregularitгes of Distribution, Cambridge Universitу Press, 1987. (1987) MR0903025
  2. CHEN W. W. L.-SKRIGANOV M. M., Davenporťs theorem in the theory of irregularities of point distribution, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 269 (2000), 339-353. MR1805869
  3. DE CLERCK L., A method for exact calculation of the stardiscrepancy of plane sets applied to the sequences of Hammersley, Monatsh. Math. 101 (1986), 261-278. (1986) Zbl0588.10059MR0851948
  4. DRMOTA M.-TICHY R. F., Sequences, Discrepancies and Applications, Lecture Notes in Math. 1651, Springer-Verlag, Berlin, 1997. (1997) Zbl0877.11043MR1470456
  5. ENTACHER K., Haar function based estimates of the star-discrepancy of plane digital nets, Monatsh. Math. 130 (2000), 99-108. Zbl0948.11030MR1767179
  6. HALTON J. H.-ZAREMBA S. K., The extreme and the L 2 discrepancies of some plane sets, Monatsh. Math. 73 (1969), 316-328. (1969) MR0252329
  7. KRITZER P., On some remarkable properties of the two-dimensional Hammersley point set in base 2 J, Théor. Nombres Bordeaux 18 (2006), 203-221. MR2245882
  8. KRITZER P.-LARCHER G.-PILLICHSHAMMER F., A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets, Ann. Mat. Pura Appl. (4) (2007) (To appear). Zbl1150.11026MR2295117
  9. KUIPERS L.-NIEDERREITER H., Uniform Distribution of Sequences, John Wileу, New York, 1974. (1974) Zbl0281.10001MR0419394
  10. LARCHER G.-PILLICHSHAMMER F., Sums of distances to the nearest integer and the discrepancy of digital nets, Acta Arith. 106 (2003), 379-408. Zbl1054.11039MR1957912
  11. MATOUŠEK J., Geometric Discrepancy, Algorithms Combin. 18, Springer, Berlin, 1999. (1999) Zbl0930.11060MR1697825
  12. NIEDERREITER H., Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. (1987) Zbl0626.10045MR0918037
  13. NIEDERREITER H., Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. (1992) Zbl0761.65002MR1172997
  14. PILLICHSHAMMER F., On the L p -discrepancy of the Hammersley Point Set, Monatsh. Math. 136 (2002), 67-79. Zbl1010.11043MR1908081
  15. ROTH K. F., On irregularities of distribution, Mathematika 1 (1954), 73-79. (1954) Zbl0057.28604MR0066435
  16. SCHMIDT W. M., Irregularities of distribution X, ln: Number Thеory and Algebra, Acadеmic Prеss, Nеw York, 1977, pp. 311-329. (1977) Zbl0373.10020MR0491574
  17. VILENKIN I. V., Plane nets of Integration, Zh. Vychisl. Mat. Mat. Fiz. 7 (1967), 189-196 [English translation in: Comput. Math. Math. Phys. 7 (1967), 258-267.] (1967) Zbl0187.10701MR0205464

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