25 citations · 135 across the 12 of their papers we have counts for
7 papers · 1 filter
QMC integration based on arbitrary (t,m,s)-nets yields optimal convergence rates on several scales of function spaces
Michael Gnewuch, Josef Dick, Lev Markhasin +1
We study the integration problem over the -dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions who…
Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions
Aicke Hinrichs, Lev Markhasin, Jens Oettershagen +1
We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces with dominating mixed smoothnes…
L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets
Lev Markhasin
Dick proved that all order digital nets satisfy optimal upper bounds of the -discrepancy. We give an alternative proof for this fact using Haar bases. Furthermore, we prov…
Discrepancy and integration in function spaces with dominating mixed smoothness
Lev Markhasin
Optimal lower bounds for discrepancy in Besov spaces with dominating mixed smoothness are known from the work of Triebel. Hinrichs proved upper bounds in the plane. In this work we…
Quasi-Monte Carlo methods for integration of functions with dominating mixed smoothness in arbitrary dimension
Lev Markhasin
In a celebrated construction, Chen and Skriganov gave explicit examples of point sets achieving the best possible -norm of the discrepancy function. We consider the discrepanc…
Discrepancy of generalized Hammersley type point sets in Besov spaces of dominating mixed smoothness
Lev Markhasin
The symmetrized Hammersley point set is known to achieve the best possible rate for the -norm of the discrepancy function. Also lower bounds for the norm in Besov spaces of do…
On lower bounds for the L_2-discrepancy
Aicke Hinrichs, Lev Markhasin
The L_2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L_2 discrepancy of arbitrary N-point sets. Our m…