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ANTS
2010
Springer
246views Algorithms» more  ANTS 2010»
13 years 11 months ago
On the Extremality of an 80-Dimensional Lattice
Abstract. We show that a specific even unimodular lattice of dimension 80, first investigated by Schulze-Pillot and others, is extremal (i.e., the minimal nonzero norm is 8). Thi...
Damien Stehlé, Mark Watkins
NA
2007
100views more  NA 2007»
13 years 7 months ago
Periodization strategy may fail in high dimensions
Abstract. We discuss periodization of smooth functions f of d variables for approximation of multivariate integrals. The benefit of periodization is that we may use lattice rules,...
Frances Y. Kuo, Ian H. Sloan, Henryk Wozniakowski
COMPUTING
2007
118views more  COMPUTING 2007»
13 years 7 months ago
The construction of good extensible Korobov rules
In this paper we introduce construction algorithms for Korobov rules for numerical integration which work well for a given set of dimensions simultaneously. The existence of such ...
Josef Dick, Friedrich Pillichshammer, Benjamin J. ...
CSC
2008
13 years 9 months ago
On the Random Walks of Geometrical Forms in Two-Dimensions
I show how to design the value of the diffusion constant D for the random walks of Squares and Triangles over their respective regular lattice in two-dimensions. By allowing moveme...
J. F. Nystrom
ORDER
2008
100views more  ORDER 2008»
13 years 7 months ago
Orthogonal Surfaces and Their CP-Orders
Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthog...
Stefan Felsner, Sarah Kappes