Explicit constructions in the classical mean squares problem in irregularities of point distribution

By W. Chen, Maxim Skriganov. 2002

98 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/fc60621e6e4fc40a333b72de85a1223dfea43002

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In Computational Theory and Mathematics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

Discrepancy Theory and Quasi-Monte Carlo Integration (2014, unknown): “The convergence rate of the randomised error for functions from the reproducing kernel Hilbert spaces considered in Section 1.3 is of order N−1(logN)(s−1)/2; see Chen and Skriganov [12], Cristea, D., and P. [14], and [31].”
Tractability of Multivariate Problems (2008, background): “A fully constructive proof was finally given in 2002 by Chen and Skriganov [30].”
MacWilliams Duality and the Rosenbloom—Tsfasman Metric (2002, methodology): “As an application of the ρ metric, we should mention a recent paper [1] by Chen and Skriganov, where explicit constructions of point sets with minimal order of the L2 discrepancy are given as codes with large weights simultaneously in the Hamming and Rosenbloom–Tsfasman metrics.”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, methodology): “Duality for digital nets was first introduced and studied by Niederreiter & Pirsic [187] and, in a more specialised setting, by Skriganov [241], see also [22].”
Walsh Series Analysis of the L2-Discrepancyof Symmetrisized Point Sets (2001, background): “Finally quite recently, Chen and Skriganov [ 1 ] gave concrete examples (not only existence results as Roth did) of point sets in arbitrary dimensions of minimal order of L2-discrepancy.”
Hyperbolic Cross Approximation (2016, background): “Based on the badic (b large) Chen-Skriganov [57] point construction CSn (which we will not discuss in detail) Markhasin [233] showed the following.”