Haar function based estimates of the star-discrepancy of plane digital nets

Monatshefte fur Mathematik

Volumn 130, Issue 2, 2000, Pages 99-108

  Entacher, Karl ^a  

^a UNIVERSITY OF SALZBURG   (Austria)

Author keywords

(t, m, s) nets; Discrepancy; Haar functions; Hammersley point set; Uniform distribution modulo one

Indexed keywords

EID: 0034355044     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006050070040     Document Type: Article

References (19)

1. Clerck L De (1986) A method for exact calculation of the stardiscrepancy of plane sets applied to the sequences of Hammersley. Monatsh Math 101: 261-278
2. Entacher K (1995) Generalized Haar function systems in the theory of uniform distribution of sequences modulo one. PhD Thesis, University of Salzburg
3. Entacher K (1998) Quasi-Monte Carlo methods for numerical integration of multivariate Haar series II. BIT 38: 283-292
4. 2 discrepancies of some plane sets. Monatsh Math 73: 316-328
5. Hellekalek P (1998) On the assessment of random and quasi-random point sets, pp 49-108
6. Hellekalek P (1994) General discrepancy estimates II: the Haar function system. Acta Arith 67: 313-322
7. Hellekalek P (1995) General discrepancy estimates III: the Erdös-Turán-Koksma inequality for the Haar function system. Monatsh Math 120: 25-45
8. Hellekalek P, Larcher G (Editors) (1998) Random and Quasi-Random Point Sets. Lect Notes Statistics 138. Berlin Heidelberg New York: Springer
9. Larcher G (1998) Digital point sets: analysis and application. In [8]. pp 167-222
10. Larcher G, Lauβ A, Niederreiter H, Schmid WCh (1996) Optimal polynomials for (t,m,s)-nets and numerical integration of multivariate Walsh series. SIAM J Numer Analysis 33: 2239-2253
11. Larcher G, Nierreiter H, Schmid WCh (1996) Digital nets and sequences constructed over finite rings and their applications to quasi-monte-carlo integration. Monatsh Math 121: 231-253
12. Morohosi H, Fushimi M (2000) A practical approach to the error estimation of quasi-monte carlo integrations. In [17], pp 377-390
13. Niederreiter H (2000) Constructions of (t,m,s)-nets. In [17], pp 70-85
14. Niederreiter H (1987) Point sets and sequences with small discrepancy. Monatsh Math 104: 273-337
15. Niederreiter H (1988) Low-discrepancy and low-dispersion sequences. J Number Theory 30: 51-70
16. Niederreiter H (1992) Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia: SIAM
17. Niederreiter H, Spanier J (eds) (2000) Monte Carlo and Quasi-Monte Carlo Methods 1998. Berlin Heidelberg New York: Springer
18. Niederreiter H, Xing Ch (1998) Nets, (t,s)-Sequences, and Algebraic Geometry, pp 267-302
19. Sobol' IM (1969) Multidimensional Quadrature Formulas and Haar Functions Moscow Izdat Nauka (in Russian)