Publications

Selected publications

Submitted manuscripts & preprints

1. On bounds between all s-numbers and widths of convex setssubmitted (2026)arXiv:2608.05024
2. Constructive discretization and approximation in reproducing kernel Hilbert spaceswith A. Chkifa, M. Dolbeault & D. KriegarXiv:2602.18719
3. How many continuous measurements are needed to learn a vector?with D. Krieg & E. NovakarXiv:2412.06468

Refereed journal papers

1. Approximation of functions: optimal sampling and complexityActa Numericawith D. Krieg · Acta Numer. 35 (2026), 273–457 (invited survey)DOIarXiv:2602.02066
2. Nonlocal techniques for the analysis of deep ReLU neural network approximationswith C. Schneider & J. Vybral · J. Mach. Learn. Res. 27:11 (2026), 1–41JMLRarXiv:2504.04847
3. Sparse grids vs. random points for high-dimensional polynomial approximationwith J. Eggl & E. Mindlberger · Adv. Comput. Math. 52:3 (2026), 44DOIarXiv:2506.24054
4. Noisy nonlinear information and entropy numberswith D. Krieg, E. Novak & L. Plaskota · J. Fourier Anal. Appl. 32:36 (2026)DOIarXiv:2510.23213
5. Sampling and entropy numbers in the uniform normJ. Complexity 92 (2026), 101992DOIarXiv:2507.20770
6. On the power of adaption and randomizationwith D. Krieg & E. Novak · Forum Math. Sigma 13 (2025), e152DOIarXiv:2406.07108
7. Sampling projections in the uniform normwith D. Krieg, K. Pozharska & T. Ullrich · J. Math. Anal. Appl. 553:2 (2026), 129873DOIarXiv:2401.02220
8. Sampling recovery in \(L_2\) and other normswith D. Krieg, K. Pozharska & T. Ullrich · Math. Comp. (2025, online)DOIarXiv:2305.07539
9. Inequalities between s-numbersAdv. Oper. Theory 9:4 (2024), 82 (Special issue in memory of A. Pietsch)DOIarXiv:2405.05509
10. On the power of iid information for linear approximationwith M. Sonnleitner · J. Appl. Numer. Anal. 1 (2023), 88–126 (invited survey)DOIarXiv:2310.12740
11. Exponential tractability of \(L_2\)-approximation with function valueswith D. Krieg, P. Siedlecki & H. Woźniakowski · Adv. Comput. Math. 49:18 (2023)DOIarXiv:2205.04141
12. A sharp upper bound for sampling numbers in \(L_2\)with M. Dolbeault & D. Krieg · Appl. Comput. Harmon. Anal. 63 (2023), 113–134DOIarXiv:2204.12621
13. Deterministic constructions of high-dimensional sets with small dispersionwith J. Vybral · Algorithmica 84 (2022), 1897–1915DOIarXiv:1901.06702
14. Function values are enough for \(L_2\)-approximation: Part IIwith D. Krieg · J. Complexity 66 (2021), 101569DOIarXiv:2011.01779
15. On the worst-case error of least squares algorithms for \(L_2\)-approximation with high probabilityJ. Complexity 60 (2020), 101484DOIarXiv:2003.11947
16. Function values are enough for \(L_2\)-approximationwith D. Krieg · Found. Comput. Math. 21 (2021), 1141–1151DOIarXiv:1905.02516
17. Random sections of ellipsoids and the power of random informationwith A. Hinrichs, D. Krieg, E. Novak & J. Prochno · Trans. Amer. Math. Soc. 374 (2021), 8691–8713DOIarXiv:1901.06639
18. On the power of random informationwith A. Hinrichs, D. Krieg, E. Novak & J. Prochno · in: Multivariate Algorithms and IBC, 43–64, De Gruyter (2020)DOIarXiv:1903.00681
19. On the fixed volume discrepancy of the Fibonacci sets in the integral normswith V. N. Temlyakov · J. Complexity 61 (2020), 101472DOIarXiv:1908.04658
20. Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaceswith C. Kacwin, J. Oettershagen & T. Ullrich · Found. Comput. Math. 21 (2021), 849–889DOIarXiv:1802.08666
21. On a multi-dimensional Poissonian pair correlation concept and uniform distributionwith A. Hinrichs, L. Kaltenböck, G. Larcher & W. Stockinger · Monatsh. Math. 190 (2019), 333–352DOIarXiv:1809.05672
22. The minimal \(k\)-dispersion of point sets in high dimensionswith A. Hinrichs, J. Prochno & J. Vybral · J. Complexity 51 (2019), 68–78DOIarXiv:1807.01492
23. A note on the dispersion of admissible latticesDiscrete Appl. Math. 257 (2019), 385–387DOIarXiv:1710.08694
24. The curse of dimensionality for numerical integration on general domainsJ. Complexity Best Paper Awardwith A. Hinrichs & J. Prochno · J. Complexity 50 (2019), 25–42DOIarXiv:1804.03957
25. Comparison of hit-and-run, slice sampling and random walk Metropoliswith D. Rudolf · J. Appl. Probab. 55 (2018), 1186–1202DOIarXiv:1505.00579
26. Lattice rules with random \(n\) achieve nearly the optimal error independently of the dimensionwith P. Kritzer, F. Y. Kuo & D. Nuyens · J. Approx. Theory 240 (2019), 96–113DOIarXiv:1706.04502
27. Digital net properties of a polynomial analogue of Frolov's constructionwith J. Dick, F. Pillichshammer, K. Suzuki & T. Yoshiki · Finite Fields Appl. 51 (2018), 325–350DOIarXiv:1712.06831
28. Reproducing kernels of Sobolev spaces on \(\mathbb{R}^d\) and applications to embedding constants and tractabilitywith E. Novak, H. Woźniakowski & S. Zhang · Anal. Appl. 16 (2018), 693–715DOIarXiv:1709.02568
29. An upper bound on the minimal dispersionwith J. Vybral · J. Complexity 45 (2018), 120–126DOIarXiv:1710.06754
30. Lattice based integration algorithms: Kronecker sequences and rank-1 latticeswith J. Dick, F. Pillichshammer, K. Suzuki & T. Yoshiki · Ann. Mat. Pura Appl. 197 (2018), 109–126DOIarXiv:1608.08687
31. A lower bound for the dispersion on the torusMath. Comput. Simulation 143 (2018), 186–190DOIarXiv:1510.04617
32. A Monte Carlo method for integration of multivariate smooth functionsSIAM J. Numer. Anal. 55 (2017), 1188–1200DOIarXiv:1604.06008
33. Product rules are optimal for numerical integration in classical smoothness spaceswith A. Hinrichs, E. Novak & H. Woźniakowski · J. Complexity 38 (2017), 39–49DOIarXiv:1604.00261
34. Complexity of oscillatory integrals on the real linewith E. Novak, H. Woźniakowski & S. Zhang · Adv. Comput. Math. 43 (2017), 537–553DOIarXiv:1511.05414
35. Change of variable in spaces of mixed smoothness and numerical integration on the unit cubewith V. K. Nguyen & T. Ullrich · Constr. Approx. 46 (2017), 69–108DOIarXiv:1511.02036
36. The role of Frolov's cubature formula for functions with bounded mixed derivativewith T. Ullrich · SIAM J. Numer. Anal. 54 (2016), 969–993DOIarXiv:1503.08846
37. On “Upper error bounds for quadrature formulas on function classes” by K. K. Frolovin: Monte Carlo and Quasi-Monte Carlo Methods, Springer Proc. Math. Stat. 163 (2016), 571–582DOIarXiv:1404.5457
38. Complexity of oscillatory integration for univariate Sobolev spaceswith E. Novak & H. Woźniakowski · J. Complexity 31 (2014), 15–41DOIarXiv:1311.1528
39. Rapid mixing of Swendsen–Wang dynamics in two dimensionsDissertationes Math. 502 (2014), 64 pp.DOIarXiv:1212.4908
40. On weak tractability of the Clenshaw–Curtis Smolyak algorithmwith A. Hinrichs & E. Novak · J. Approx. Theory 183 (2014), 31–44DOIarXiv:1301.4055
41. Structure and eigenvalues of heat-bath Markov chainswith M. Dyer & C. Greenhill · Linear Algebra Appl. 454 (2014), 57–71DOIarXiv:1309.0360
42. The curse of dimensionality for numerical integration of smooth functions IIwith A. Hinrichs, E. Novak & H. Woźniakowski · J. Complexity 30 (2014), 117–143DOIarXiv:1304.3372
43. The curse of dimensionality for numerical integration of smooth functionswith A. Hinrichs, E. Novak & H. Woźniakowski · Math. Comp. 83 (2014), 2853–2863DOIarXiv:1211.0871
44. Swendsen–Wang is faster than single-bond dynamicsSIAM J. Discrete Math. 28 (2014), 37–48DOIarXiv:1201.5793
45. Positivity of hit-and-run and related algorithmswith D. Rudolf · Electron. Commun. Probab. 18 (2013), no. 49, 1–8DOIarXiv:1212.4512
46. Comparison of Swendsen–Wang and heat-bath dynamicsRandom Structures Algorithms 42 (2013), 520–535DOIarXiv:1105.3665
47. Exact sampling for the Ising model at all temperaturesMonte Carlo Methods Appl., 223–233, De Gruyter (2013)arXiv:1012.3944

Theses

1. Random vs. optimal data for high-dimensional approximationHabilitation thesis, JKU Linz, 2023
2. Rapid mixing of Swendsen–Wang dynamics in two dimensionsPhD dissertation, FSU Jena, 2012
3. Explicit error bounds and comparison of importance sampling and the Metropolis algorithmDiploma thesis (in German), FSU Jena, 2009