| Title:
|
Points sets with low $L_p$ discrepancy (English) |
| Author:
|
Kritzer, Peter |
| Author:
|
Pillichshammer, Friedrich |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
11-32 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11K06 |
| MSC:
|
11K38 |
| idZBL:
|
Zbl 1153.11037 |
| idMR:
|
MR2357804 |
| . |
| Date available:
|
2009-09-25T14:35:57Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136938 |
| . |
| Reference:
|
[1] BECK J.-CHEN W. W. L.: Irregularitгes of Distribution.Cambridge Universitу Press, 1987. MR 0903025 |
| Reference:
|
[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. MR 1805869 |
| Reference:
|
[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. Zbl 0588.10059, MR 0851948 |
| Reference:
|
[4] DRMOTA M.-TICHY R. F.: Sequences, Discrepancies and Applications.Lecture Notes in Math. 1651, Springer-Verlag, Berlin, 1997. Zbl 0877.11043, MR 1470456 |
| Reference:
|
[5] ENTACHER K.: Haar function based estimates of the star-discrepancy of plane digital nets.Monatsh. Math. 130 (2000), 99-108. Zbl 0948.11030, MR 1767179 |
| Reference:
|
[6] HALTON J. H.-ZAREMBA S. K.: The extreme and the $L^2$ discrepancies of some plane sets.Monatsh. Math. 73 (1969), 316-328. MR 0252329 |
| Reference:
|
[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. MR 2245882 |
| Reference:
|
[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). Zbl 1150.11026, MR 2295117 |
| Reference:
|
[9] KUIPERS L.-NIEDERREITER H.: Uniform Distribution of Sequences.John Wileу, New York, 1974. Zbl 0281.10001, MR 0419394 |
| Reference:
|
[10] LARCHER G.-PILLICHSHAMMER F.: Sums of distances to the nearest integer and the discrepancy of digital nets.Acta Arith. 106 (2003), 379-408. Zbl 1054.11039, MR 1957912 |
| Reference:
|
[11] MATOUŠEK J.: Geometric Discrepancy.Algorithms Combin. 18, Springer, Berlin, 1999. Zbl 0930.11060, MR 1697825 |
| Reference:
|
[12] NIEDERREITER H.: Point sets and sequences with small discrepancy.Monatsh. Math. 104 (1987), 273-337. Zbl 0626.10045, MR 0918037 |
| Reference:
|
[13] NIEDERREITER H.: Random Number Generation and Quasi-Monte Carlo Methods.SIAM, Philadelphia, 1992. Zbl 0761.65002, MR 1172997 |
| Reference:
|
[14] PILLICHSHAMMER F.: On the $L_p$-discrepancy of the Hammersley Point Set.Monatsh. Math. 136 (2002), 67-79. Zbl 1010.11043, MR 1908081 |
| Reference:
|
[15] ROTH K. F.: On irregularities of distribution.Mathematika 1 (1954), 73-79. Zbl 0057.28604, MR 0066435 |
| Reference:
|
[16] SCHMIDT W. M.: Irregularities of distribution X.ln: Number Thеory and Algebra, Acadеmic Prеss, Nеw York, 1977, pp. 311-329. Zbl 0373.10020, MR 0491574 |
| Reference:
|
[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.] Zbl 0187.10701, MR 0205464 |
| . |
