|
A lower bound for rank 2 lattice rules
Author(s):
Friedrich
Pillichshammer.
Journal:
Math. Comp.
73
(2004),
853-860.
MSC (2000):
Primary 11K06, 65D32, 41A55
Posted:
July 29, 2003
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give a lower bound for a quality measure of rank 2 lattice rules which shows that an existence result of Niederreiter is essentially best possible.
References:
-
- 1.
- Hlawka, E.: Zur angenäherten Berechnung mehrfacher Integrale. Monatsh. Math. 66: 140-151, 1962. MR 26:888
- 2.
- Korobov, N.M.: Numbertheoretical Methods in Approximate Analysis. Moscow: Fizmatgiz. 1963. (In Russian.) MR 28:716
- 3.
- Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. John Wiley, New York, 1974. MR 54:7415
- 4.
- Larcher, G.: A Best Lower Bound for Good Lattice Points. Monatsh. Math. 104: 45-51, 1987. MR 89f:11103
- 5.
- Niederreiter, H.: Existence of Good Lattice Points in the Sense of Hlawka. Monatsh. Math. 86: 203-219, 1978. MR 80e:10039
- 6.
- Niederreiter, H.: The Existence of Efficient Lattice Rules for Multidimensional Numerical Integration. Math. Comp. 58: 305-314 and S7-S16, 1992. MR 92e:65023
- 7.
- Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. No. 63 in CBMS-NSF Series in Applied Mathematics. SIAM, Philadelphia, 1992. MR 93h:65008
- 8.
- Niederreiter, H., Sloan, I.H.: Lattice rules for multiple integration and discrepancy. Math. Comp. 54: 303-312, 1990. MR 90f:65036
- 9.
- Sloan, I.H., Joe, S.: Lattice Methods for Multiple Integration. Oxford Univ. Press, New York and Oxford, 1994. MR 98a:65026
- 10.
- Sloan, I.H., Lyness, J.N.: Lattice rules: Projection regularity and unique representations. Math. Comp. 54: 649-660, 1990. MR 91a:65062
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(2000):
11K06, 65D32, 41A55
Retrieve articles in all Journals with MSC
(2000):
11K06, 65D32, 41A55
Additional Information:
Friedrich
Pillichshammer
Affiliation:
Institut für Analysis, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria
Email:
friedrich.pillichshammer@jku.at
DOI:
10.1090/S0025-5718-03-01596-5
PII:
S 0025-5718(03)01596-5
Keywords:
Rank 2 lattice rule,
quadrature error bound
Received by editor(s):
August 5, 2002
Received by editor(s) in revised form:
November 8, 2002
Posted:
July 29, 2003
Additional Notes:
Supported by the Austrian Research Foundation (FWF), project S 8305.
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org