Research Group of Dr. T. Ullrich
Institute for Numerical Simulation

Welcome to the research group of Dr. Tino Ullrich

Dr. Tino Ullrich
Address: Institut für Numerische Simulation
Wegelerstr. 6
53115 Bonn
Office: We6 6.015
Phone: +49 228 73 3430


Workshop "Challenges in Optimal Recovery and Hyperbolic Cross Approximation"

from February 18th to February 22nd 2019 organized by Feng Dai (Alberta), Erich Novak (Jena), Vladimir Temlyakov (South Carolina) and Tino Ullrich (Bonn). Embedded in the INI Programme "Approximation, Sampling and Compression in Data Science" from January 3rd to June 26th, 2019, at Isaac Newton Institute for Mathematical Sciences in Cambridge (UK).

Invited Speaker at NAFSA 11 in Prague 2018

Tino Ullrich will be Invited Speaker at the 11th International Conference on Nonlinear Analysis, Function Spaces and Applications in Prague (CZ), July 9-14, 2018.

Interim W3-Professor "Applied Analysis" at Osnabrück University

From April 2017 to September 2017 I was Interim Professor (W3) for Applied Analysis at Osnabrück University.

IBC workshop at FoCM 2017

Frances Kuo, Erich Novak and Tino Ullrich will be the organizers of the Information based Complexity workshop at the FoCM 2017, July 10-19th, Barcelona.

Mini-symposium on Preasymptotics at MCQMC 2016

For this year's MCQMC conference, held at Stanford university, Thomas Kühn (Leipzig) and Tino Ullrich have organized a mini-symposium on preasymptotics for multivariate approximation problems.

Plenary talk at SGA 2016

Tino Ullrich will be plenary speaker at the 4th Workshop on Sparse Grids and Applications in Miami (FL), October 4-7, 2016.

Advanced course on Hyperbolic Cross Approximation

Here you find the slides for the advanced course on Hyperbolic Cross Approximation, which Tino Ullrich gave together with Vladimir N. Temlyakov at the CRM Barcelona in May 2016.

IBC Young Researcher Award 2014

Tino Ullrich is the winner of the Information Based Complexity Young Researcher Award 2014.

Group publications (since 2013)


[1] C. Kacwin, J. Oettershagen, M. Ullrich, and T. Ullrich. Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces. Preprint Uni Bonn, pages 1-40, 2018.
bib | .pdf 1 ]


[1] D. Dung, V. N. Temlyakov, and T. Ullrich. Hyperbolic Cross Approximation. Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer, to appear.
bib | arXiv ]

Journal Papers:

[1] G. Garrigós, A. Seeger, and T. Ullrich. The Haar system as a Schauder basis in spaces of Hardy-Sobolev type. Journal of Fourier Analysis and Applications, to appear. arXiv:1609.08225 [math.CA].
bib | arXiv ]
[2] S. Dirksen and T. Ullrich. Gelfand numbers related to structured sparsity and Besov space embeddings with small mixed smoothness. J. Complexity, to appear. arXiv:1702.06781 [cs.IT].
bib | arXiv ]
[3] G. Byrenheid, V. K. Nguyen, and R. J. Kunsch. Monte-Carlo methods for uniform approximation on periodic Sobolev spaces with mixed smoothness . J. Complexity, to appear. arXiv:1709.03321.
bib | arXiv ]
[4] H. Kempka, M. Schäfer, and T. Ullrich. General coorbit space theory for quasi-Banach spaces and inhomogeneous function spaces with variable smoothness and integrability. Journal of Fourier Analysis and Applications, 23(6):1348-1407, 2017.
bib ]
[5] A. Seeger and T. Ullrich. Haar projection numbers and failure of unconditional convergence in Sobolev spaces. Mathematische Zeitschrift, 285:91 - 119, 2017.
bib | arXiv ]
[6] G. Byrenheid, L. Kämmerer, T. Ullrich, and T. Volkmer. Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness. Num. Math., 136:993-1034, 2017.
bib | arXiv | .pdf 1 ]
[7] V. K. Nguyen, M. Ullrich, and T. Ullrich. Change of variable in spaces of mixed smoothnes and numerical integration of multivariate functions on the unit cube. Constructive Approximation, 46:69-108, 2017.
bib | arXiv | .pdf 1 ]
[8] A. Seeger and T. Ullrich. Lower bounds for Haar projections: deterministic examples. Constructive Approximation, 46:227–242, 2017.
bib | arXiv | .pdf 1 ]
[9] G. Byrenheid and T. Ullrich. Optimal sampling recovery of mixed order Sobolev embeddings via discrete Littlewood-Paley type characterizations. Anal. Math., 43(2):133-191, 2017.
bib | http ]
[10] C. Kacwin, J. Oettershagen and T. Ullrich. On the orthogonality of the Chebyshev-Frolov lattice and applications. Monatsh. Math., 184(3):425-441, 2017.
bib | http ]
[11] G. Garrigós, A. Seeger, and T. Ullrich. On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type. Analysis Mathematica, 43:267-278, 2017.
bib | arXiv ]
[12] G. Byrenheid, D. Dũng, W. Sickel, and T. Ullrich. Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in Hγ. J. Approx. Theory, 207:207-231, 2016.
bib | arXiv | .pdf 1 ]
[13] A. Hinrichs, L. Markhasin, J. Oettershagen, and T. Ullrich. Optimal quasi-Monte Carlo rules on higher order digital nets for the numerical integration of multivariate periodic functions. Num. Math, 134:163-196, 2016.
bib | arXiv ]
[14] M. Ullrich and T. Ullrich. The role of Frolov's cubature formula for functions with bounded mixed derivative. SIAM Journ. on Numerical Analysis, 54, No. 2:969-993, 2016.
bib | arXiv | .pdf 1 ]
[15] T. Kühn, S. Mayer, and T. Ullrich. Counting via entropy: new preasymptotics for the approximation numbers of Sobolev embeddings. SIAM Journ. on Numerical Analysis, 54(6):3625 - 3647, 2016.
bib | arXiv | .pdf 1 ]
[16] D. Dung and T. Ullrich. Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square. Math. Nachrichten, 288:743-762, 2015.
bib | arXiv | .pdf 1 ]
[17] T. Kühn, W. Sickel, and T. Ullrich. Approximation of mixed order Sobolev functions on the d-torus – asymptotics, preasymptotics and d-dependence. Constructive Approximation, 42:353-398, 2015.
bib | arXiv | .pdf 1 ]
[18] S. Mayer, T. Ullrich, and J. Vybiral. Entropy and sampling numbers of classes of ridge functions. Constructive Approximation, 42:231-264, 2015.
bib | DOI | arXiv | .pdf 1 ]
[19] A. Hinrichs and S. Mayer. Entropy numbers of spheres in Banach and quasi-Banach spaces. J. Approx. Theory, 200:144-152, 2015.
bib | arXiv | .pdf 1 ]
[20] M. Gnewuch, S. Mayer, and K. Ritter. On Weighted Hilbert Spaces and Integration of Functions of Infinitely Many Variables. J. Complexity, 30(2):29-47, 2014.
bib | .pdf 1 ]
[21] T. Ullrich. Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square. J. Complexity, 30:72-94, 2014.
bib | .pdf 1 ]
[22] T. Kühn, W. Sickel, and T. Ullrich. Approximation numbers of Sobolev embeddings-sharp constants and tractability. J. Complexity, 30:95-116, 2014.
bib | .pdf 1 ]
[23] D. Dung and T. Ullrich. N-widths and ε-dimensions for high-dimensional approximations. Found. Comput. Math., 13:965-1003, 2013.
bib | .pdf 1 ]

Conference contributions:

[1] S. Dirksen and T. Ullrich. Gelfand numbers, structured sparsity and Besov space embeddings with small mixed smoothness. 2017 International Conference on Sampling Theory and Applications (SampTA), pages 400-403, 2017.
bib ]

Other Reports:

[1] S. Mayer. Reconstruction of ridge functions from function values. Oberwolfach Report No. 6, 2015. Extended abstract.
bib | DOI | .pdf 1 ]
[2] S. Mayer. Tractability results for classes of ridge functions. Oberwolfach Report No. 49, 2013. Extended abstract.
bib | DOI | .pdf 1 ]