Points sets with low L p discrepancy

Peter Kritzer; Friedrich Pillichshammer

Mathematica Slovaca (2007)

  • Volume: 57, Issue: 1, page 11-32
  • ISSN: 0139-9918

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.