Geometric Discrepancy: An Illustrated Guide

By Jirí Matousek. 2009

368 citations recorded by the source corpus.

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Citations in the corpus

Quadrature rules and distribution of points on manifolds (2010, background): “See [4] or [23], and for other relations between quadrature a nd discrepancy on spheres, see also [2].”
A semi-algebraic version of Zarankiewicz's problem (2014, methodology): “The proof of Lemma 2.5 can be regarded as a modiﬁcation of Chazelle’s argument (see [30]), but we give a self-contained presentation.”
Automated Construction of Robotic Manipulation Programs (2010, methodology): “To sample R(3), we use a lattice where the three axes are prime with respect to the field of fractions on the integers Z [Matousek (1999)].”
Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands (2010, unknown): “ for future research. Since the classical scrambling by Owen [15] is computationally to expensive, variations of this scrambling scheme have been introduced which can easily be implemented. Matousek [11, 12] describes an alternative scrambling which uses less permutations and is therefore easier to ”
Practical Coreset Constructions for Machine Learning (2017, background): “However, this bound corresponds to a generalization of the primal shattering dimension in classical VC theory to continuous loss functions [Har-Peled, 2011, Matousek, 2009], and is hence not the one required by Li et al. [2001].”
Optimal private halfspace counting via discrepancy (2012, methodology): “Let the mechanisms M 1 , . . . , M s satisfy, respectively, ( ε 1 , δ 1 ) , . . . , ( ε s , δ s ) diﬀerential privacy.”