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07/21/2023
Bernstein approximation and beyond: proofs by means of elementary probability theory
Bernstein polynomials provide a constructive proof for the Weierstrass a...
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04/28/2023
Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation
We study numerical integration over bounded regions in ℝ^s, s≥1 with res...
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03/03/2023
The curse of dimensionality for the L_p-discrepancy with finite p
The L_p-discrepancy is a quantitative measure for the irregularity of di...
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01/17/2023
The BMO-discrepancy suffers from the curse of dimensionality
We show that the minimal discrepancy of a point set in the d-dimensional...
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01/04/2023
Grid-Based Decimation for Wavelet Transforms with Stably Invertible Implementation
The constant center frequency to bandwidth ratio (Q-factor) of wavelet t...
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12/12/2022
Tractability of L_2-approximation and integration in weighted Hermite spaces of finite smoothness
In this paper we consider integration and L_2-approximation for function...
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12/12/2022
Optimal periodic L_2-discrepancy and diaphony bounds for higher order digital sequences
We present an explicit construction of infinite sequences of points (x_0...
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01/24/2022
Tractability of approximation in the weighted Korobov space in the worst-case setting
In this paper we consider L_p-approximation, p ∈{2,∞}, of periodic funct...
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02/02/2021
Tractability of approximation in the weighted Korobov space in the worst-case setting – a complete picture
In this paper, we study tractability of L_2-approximation of one-periodi...
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10/09/2020
On the relation of the spectral test to isotropic discrepancy and L_q-approximation in Sobolev spaces
This paper is a follow-up to the recent paper "A note on isotropic discr...
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10/07/2020
A note on Korobov lattice rules for integration of analytic functions
We study numerical integration for a weighted Korobov space of analytic ...
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09/15/2020
Weighted integration over a cube based on digital nets and sequences
Quasi-Monte Carlo (QMC) methods are equal weight quadrature rules to app...
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01/31/2020
Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals
We study the approximation of compact linear operators defined over cert...
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01/16/2020
On Quasi-Monte Carlo Methods in Weighted ANOVA Spaces
In the present paper we study quasi-Monte Carlo rules for approximating ...
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01/07/2020
A note on the periodic L_2-discrepancy of Korobov's p-sets
We study the periodic L_2-discrepancy of point sets in the d-dimensional...
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10/28/2019