Nets constructed over finite fields and the numerical integration of multivariate Walsh series

Finite Fields and their Applications

Volumn 2, Issue 3, 1996, Pages 304-320

  Larcher, Gerhard ^a   Wolf, Reinhard ^a  

^a UNIVERSITY OF SALZBURG   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030186240     PISSN: 10715797     EISSN: None     Source Type: Journal    
DOI: 10.1006/ffta.1996.0019     Document Type: Article

References (13)

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2. 2. G. Larcher, A class of low-dicsrepancy point-sets and its application to numerical integration by number-theoretical methods, in "Österreichisch-Ungarisch-Slowakisches Kolloquium über Zahlentheorie" (F. Halter-Koch and R. Tichy, Eds.), pp. 69-80, Grazer Math. Ber., Vol. 318, Karl-Franzens-Univ. Press, Graz, 1993.
3. 3. G. Larcher, A. Lauβ, H. Niederreiter, and W. Ch. Schmid, Optimal polynomials for (t, m, s)-nets and numerical integration of multivariate Walsh series, SIAM J. Numer. Anal. to appear.
4. 4. G. Larcher, H. Niederreiter, and W. Ch. Schmid, Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration, Monatsh. Math., to appear.
5. 5. G. Larcher and W. Ch. Schmid, Multivariate Walsh series, digital nets and quasi-Monte Carlo integration, in "Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (Las Vegas, 1994)," (H. Niederreiter and P. J.-S. Shiue, Eds.), pp. 252-262, Lecture Notes in Statistics, Vol. 106, Springer, New York, 1995.
6. 6. G. Larcher, W. Ch. Schmid, and R. Wolf, Representation of functions as Walsh series to different bases and an application to the numerical integration of high-dimensional Walsh series, Math. Comp. 63 (1994), 701-716.
7. 7. G. Larcher, W. Ch. Schmid, and R. Wolf, Quasi-Monte Carlo methods for the numerical integration of multivariate Walsh series, Math. Comp. Modelling, to appear.
8. 8. G. Larcher and C. Traunfellner, On the numerical integration of Walsh series by number-theoretic methods, Math. Comp. 63 (1994), 277-291.
9. 9. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
10. 10. H. Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), 51-70.
11. 11. H. Niederreiter, "Random Number Generation and Quasi-Monte Carlo Methods," CBMS-NSF Series in Applied Mathematics, Vol. 63, SIAM, Philadelphia, 1992.
12. 12. F. Schipp, W. R. Wade, and P. Simon, "Walsh Series. An Introduction to Dyadic Harmonic Analysis," Hilger, Bristol/New York, 1990.
13. 13. I. M. Sobol, The distribution of points in a cube and the approximate evaluation of integrals, Ž. Vyčisl. Mat. i Mat Fiz. 7 (1967), 784-802. [in Russian]