Master of ScienceDepartment of MathematicsCraig SpencerThis paper introduces the basic elements of geometric discrepancy theory. After some background we discuss lower bounds for two problems, Schmidt’s theorem giving a lower bound for convex sets and Roth’s orthogonal method for the lower bound of the L₂ discrepancy of axis-parallel rectangles in the unit square. Then we introduce two sets with low worst-case discrepancy, the Van der Corput set for two dimensions and the Halton-Hammersley set for arbitrary dimension
AbstractTheL2-discrepancy for anchored axis-parallel boxes has been used in several recent computati...
Let R be a set of red points and B a set of blue points on the plane. In this paper we introduce a n...
Let B 2 denote the family of all circular discs in the plane. We prove that the discrepancy for the ...
Master of ScienceDepartment of MathematicsCraig SpencerThis paper introduces the basic elements of g...
The discrepancy of a set-system is the minimum number d for which the vertices can be 2-coloured red...
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of po...
AbstractThe L2-discrepancy measures the irregularity of the distribution of a finite point set. In t...
In the present paper, we study the geometric discrepancy with respect to families of rotated rectang...
We study the problem of discrepancy of finite point sets in the unit square with respect to convex p...
discrepancy in numerical analysis and statistics Josef Dick∗ In this paper we discuss various connec...
AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to ...
Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling. D...
Recently, there have been several new developments in discrepancy theory based on connections to sem...
The partial coloring method is one of the most powerful and widely used method in combinatorial disc...
Let 3[0,1]NA be a set of cardinality N. Define the Discrepancy Function associated to NA as follow...
AbstractTheL2-discrepancy for anchored axis-parallel boxes has been used in several recent computati...
Let R be a set of red points and B a set of blue points on the plane. In this paper we introduce a n...
Let B 2 denote the family of all circular discs in the plane. We prove that the discrepancy for the ...
Master of ScienceDepartment of MathematicsCraig SpencerThis paper introduces the basic elements of g...
The discrepancy of a set-system is the minimum number d for which the vertices can be 2-coloured red...
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of po...
AbstractThe L2-discrepancy measures the irregularity of the distribution of a finite point set. In t...
In the present paper, we study the geometric discrepancy with respect to families of rotated rectang...
We study the problem of discrepancy of finite point sets in the unit square with respect to convex p...
discrepancy in numerical analysis and statistics Josef Dick∗ In this paper we discuss various connec...
AbstractWe study the problem of discrepancy of finite point sets in the unit square with respect to ...
Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling. D...
Recently, there have been several new developments in discrepancy theory based on connections to sem...
The partial coloring method is one of the most powerful and widely used method in combinatorial disc...
Let 3[0,1]NA be a set of cardinality N. Define the Discrepancy Function associated to NA as follow...
AbstractTheL2-discrepancy for anchored axis-parallel boxes has been used in several recent computati...
Let R be a set of red points and B a set of blue points on the plane. In this paper we introduce a n...
Let B 2 denote the family of all circular discs in the plane. We prove that the discrepancy for the ...