Walsh series analysis of the L2-discrepancy of symmetrisized point sets

Monatshefte fur Mathematik

Volumn 132, Issue 1, 2001, Pages 1-18

  Larcher, Gerhard ^a   Pillichshammer, Friedrich ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Digital nets; L2 discrepancy; Walsh series analysis

Indexed keywords

EID: 0035661410     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006050170054     Document Type: Article

References (20)

1. Chen WWL, Skriganov MM (2000) Explicit constructions in the classical mean squares problem in irregularities of point distribution. Preprint
2. Davenport H (1956) Note on irregularities of distribution. Mathematika 3: 131-135
3. Faure H (1982) Discrepance de suites associés un systéme de numération (en dimension s). Acta Arith 41: 337-351
4. 2 discrepancies of some plane sets. Monatsh Math 73: 316-328
5. Hellekalek H (1994) General discrepancy estimates: the Walsh function system. Acta Arith 67: 313-322
6. Larcher G (1998) Digital point sets: analysis and application. In: Hellekalek P, Larcher G (eds) Random and Quasi-Random Point Sets. Lect Notes Statistics 138, pp 167-222. Berlin Heidelberg New York: Springer
7. Larcher G, Niederreiter H, Schmid WCh (1996) Digital Nets and Sequences Constructed over Finite Rings and their Application to Quasi-Monte Carlo Integration. Monatsh Math 121: 231-253
8. 2-discrepancy of the Sobol-Faure-Niederreiter Net in Dimension 3. Preprint, Univ Linz
9. Niederreiter H (1987) Point sets and sequences with small discrepancy. Monatsh Math 104: 273-337
10. Niederreiter H (1992) Random Number Generation and Quasi-Monte Carlo Methods Philadelphia: SIAM
11. Pirsic G (1997) Embedding theorems and numerical integration of Walsh series over groups. PhD Thesis, University of Salzburg
12. 2 discrepancy of a class of infinite sequences CR Acad Sci Bulgare 36: 37-40
13. Proinov PD (1988) Symmetrization of the van der Corput generalized sequences Proc Janan Acad 64, Ser A: 159-162
14. Roth KF (1954) On irregularities of distribution. Mathematika 1: 73-79
15. Roth KF (1979) On irregularities of distribution III. Acta Arith 35: 373-384
16. Roth KF (1980) On irregularities of distribution IV. Acta Arith 37: 67-75
17. Schipp F, Wade WR, Simon P, Pál J (1990) Walsh Series. An Introduction to Dyadic Harmonic Analysis. Bristol New York: Adam Hilger
18. Sobol IM (1967) The distribution of points in a cube and the approximate evaluation of integrals. Zh Vychisl Mat i Mat Fiz 7: 784-802 (In Russian)
19. White BE (1975) Mean-square discrepancy of the Hammersley and Zaremba sequences for arbitrary radix. Monatsh Math 80: 219-229
20. Wozniakowski H (1991) Average case complexity of multivariate integration. Bull Amer Math Soc New Series 24: 185-194