TY - JOUR
T1 - Discrepancy estimates based on Haar functions
AU - Entacher, K.
N1 - Cited By :1
Export Date: 14 December 2023
CODEN: MCSID
Correspondence Address: Entacher, K.; School of Telecommunications Eng., , Salzburg, Austria; email: [email protected]
Funding details: Austrian Science Fund, FWF, P12441-MAT, P12654-MAT
Funding text 1: Research supported by the Austrian Science Fund (FWF), projects P12441-MAT and P12654-MAT.
References: Entacher, K., (1995) Generalized Haar function systems in the theory of uniform distribution of sequences modulo one, , Ph.D. thesis, University of Salzburg; Entacher, K., Generalized Haar function systems, digital nets and quasi-Monte Carlo integration (1996) Wavelet Applications III, Proceedings of the SPIE 2762, , H.H. Szu (Ed.); Entacher, K., Quasi-Monte Carlo methods for numerical integration of multivariate Haar series II (1998) BIT, 38 (2), pp. 283-292; Halton, J.H., Zaremba, S.K., The extreme and L2 discrepancy of some plane sets (1969) Monatsh. Math., 73, pp. 316-328; Hellekalek, P., General discrepancy estimates: The Walsh function system (1994) Acta Arith., 67, pp. 209-218; Hellekalek, P., General discrepancy estimates II: The Haar function system (1994) Acta Arith., 67, pp. 313-322; Hellekalek, P., General discrepancy estimates III: The Erdös-Turán-Koksma inequality for the Haar function system (1995) Monatsh. Math., 120, pp. 25-45; Larcher, G., Lauß, A., Niederreiter, H., Schmid, W.Ch., Optimal polynomials for (t, m, s)-nets and numerical integration of Walsh series (1996) SIAM J. Num. Anal., 33, pp. 2239-2253; Larcher, G., Niederreiter, H., Schmid, W.Ch., Digital nets and sequences constructed over finite rings and their applications to Quasi-Monte Carlo Integration (1996) Monatsh. Math., 121, pp. 231-253; Larcher, G., Traunfellner, C., On the numerical integration of Walsh-series by number-theoretical methods (1994) Math. Comp., 63, pp. 277-291; Niederreiter, H., Pseudo-random numbers and optimal coefficients (1977) Adv. Math., 26, pp. 99-181; Niederreiter, H., Point sets and sequences with small discrepancy (1987) Monatsh. Math., 104, pp. 273-337; Niederreiter, H., Low-discrepancy and low-dispersion sequences (1988) J. Num. Theory, 30, pp. 51-70; Niederreiter, H., (1992) Random Number Generation and Quasi-Monte Carlo Methods, , SIAM, Philadelphia; Niederreiter, H., Pseudorandom vector generation by the inversive method (1994) ACM Trans. Modeling Comput. Simulation, 4, pp. 191-212; Niederreiter, H., Xing, Ch., Nets, (t, s)-sequences and algebraic geometry (1998) Lecture Notes in Statistics, 138, pp. 267-302. , P. Hellekalek, G. Larcher (Eds.), Random and Quasi-Random Point Sets, Springer, New York; Sobol', I.M., (1969) Multidimensional Quadrature Formulas and Haar Functions, , Izdat, Nauka, Moscow (in Russian)
PY - 2001
Y1 - 2001
N2 - We present a technique to estimate the star-discrepancy of (t, m, s)-nets using generalized Haar function systems and apply this technique to obtain upper bounds for the star-discrepancy of special digital (t, m, s)-nets in base 2 and dimension s=2.
AB - We present a technique to estimate the star-discrepancy of (t, m, s)-nets using generalized Haar function systems and apply this technique to obtain upper bounds for the star-discrepancy of special digital (t, m, s)-nets in base 2 and dimension s=2.
KW - (t, m, s)-nets
KW - Haar functions
KW - Hammersley point set
KW - Low-discrepancy point sets
KW - Quasi-Monte Carlo methods
KW - Star-discrepancy
KW - Weyl sums
KW - Functions
KW - Monte Carlo methods
KW - Theorem proving
KW - Hammersley point sets
KW - Computational complexity
U2 - 10.1016/S0378-4754(00)00245-7
DO - 10.1016/S0378-4754(00)00245-7
M3 - Article
SN - 0378-4754
VL - 55
SP - 49
EP - 57
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
IS - 1-3
ER -