Research Group of Prof. Dr. A. Uschmajew
Institute for Numerical Simulation
maximize

Prof. Dr. André Uschmajew

Prof. Dr. André Uschmajew
Address: Institut für Numerische Simulation
Wegelerstr. 6
53115 Bonn
Germany
Office: We6 6.019
Phone: +49 228 73 4091
E-Mail: uschmajew.ins.uni-bonn.de
See also: http://www.hcm.uni-bonn.de/people/profile/andre-uschmajew/

Teaching

Publications

Preprints:

[1] Z. Li, Y. Nakatsukasa, T. Soma, and A. Uschmajew. On orthogonal tensors and best rank-one approximation ratio. July 2017. INS Preprint No. 1707.
bib | arXiv | .pdf 1 ]
[2] S. Hosseini and A. Uschmajew. A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization. Oct. 2016. INS Preprint No. 1624. Extended and revised version, March 2017.
bib | .pdf 1 ]

Journal Papers:

[1] W. Hackbusch, D. Kressner, and A. Uschmajew. Perturbation of higher-order singular values. SIAM J. Appl. Algebra Geom., 1(1):374-387, 2017.
bib | DOI | .pdf 1 ]
[2] W. Hackbusch and A. Uschmajew. On the interconnection between the higher-order singular values of real tensors. Numer. Math., 135(3):875-894, 2017.
bib | DOI | .pdf 1 ]
[3] S. Hosseini and A. Uschmajew. A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds. SIAM J. Optim., 27(1):173-189, 2017.
bib | DOI | .pdf 1 ]
[4] Y. Nakatsukasa, T. Soma, and A. Uschmajew. Finding a low-rank basis in a matrix subspace. Math. Program., 162(1-2, Ser. A):325-361, 2017.
bib | DOI | arXiv | .pdf 1 ]
[5] M. Bachmayr, R. Schneider, and A. Uschmajew. Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. Found. Comput. Math., 16(6):1423-1472, 2016.
bib | DOI | .pdf 1 ]
[6] L. Karlsson, D. Kressner, and A. Uschmajew. Parallel algorithms for tensor completion in the CP format. Parallel Comput., 57:222-234, 2016.
bib | DOI | .pdf 1 ]
[7] D. Kressner and A. Uschmajew. On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems. Linear Algebra Appl., 493:556-572, 2016.
bib | DOI | arXiv | .pdf 1 ]
[8] Z. Li, A. Uschmajew, and S. Zhang. On convergence of the maximum block improvement method. SIAM J. Optim., 25(1):210-233, 2015.
bib | DOI | .pdf 1 ]
[9] R. Schneider and A. Uschmajew. Convergence results for projected line-search methods on varieties of low-rank matrices via Lojasiewicz inequality. SIAM J. Optim., 25(1):622-646, 2015.
bib | DOI | arXiv | .pdf 1 ]
[10] A. Uschmajew. A new convergence proof for the higher-order power method and generalizations. Pac. J. Optim., 11(2):309-321, 2015.
bib | arXiv | .html | .pdf 1 ]
[11] R. Schneider and A. Uschmajew. Approximation rates for the hierarchical tensor format in periodic Sobolev spaces. J. Complexity, 30(2):56-71, 2014.
bib | DOI | .pdf 1 ]
[12] T. Rohwedder and A. Uschmajew. On local convergence of alternating schemes for optimization of convex problems in the tensor train format. SIAM J. Numer. Anal., 51(2):1134-1162, 2013.
bib | DOI | .pdf 1 ]
[13] A. Uschmajew and B. Vandereycken. The geometry of algorithms using hierarchical tensors. Linear Algebra Appl., 439(1):133-166, 2013.
bib | DOI | .pdf 1 ]
[14] S. R. Chinnamsetty, H. Luo, W. Hackbusch, H.-J. Flad, and A. Uschmajew. Bridging the gap between quantum Monte Carlo and F12-methods. Chem. Phys., 401:36-44, 2012.
bib | DOI | .pdf 1 ]
[15] A. Uschmajew. Local convergence of the alternating least squares algorithm for canonical tensor approximation. SIAM J. Matrix Anal. Appl., 33(2):639-652, 2012.
bib | DOI | .pdf 1 ]
[16] A. Uschmajew. Regularity of tensor product approximations to square integrable functions. Constr. Approx., 34(3):371-391, 2011.
bib | DOI | .pdf 1 ]
[17] A. Uschmajew. Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations. Numer. Math., 115(2):309-331, 2010.
bib | DOI | .pdf 1 ]

Proceeding Papers:

[1] A. Uschmajew. Some results concerning rank-one truncated steepest descent directions in tensor spaces. In 2015 International Conference on Sampling Theory and Applications (SampTA), pages 415-419, 2015.
bib | DOI | .pdf 1 ]
[2] A. Uschmajew and B. Vandereycken. Greedy rank updates combined with Riemannian descent methods for low-rank optimization. In 2015 International Conference on Sampling Theory and Applications (SampTA), pages 420-424, 2015.
bib | DOI | .pdf 1 ]
[3] A. Uschmajew and B. Vandereycken. Line-search methods and rank increase on low-rank matrix varieties. In Proceedings of the 2014 International Symposium on Nonlinear Theory and its Applications (NOLTA2014), pages 52-55, 2014.
bib | .pdf 1 ]
[4] A. Uschmajew, D. Kressner, and M. Steinlechner. Low-rank tensor methods with subspace correction for symmetric eigenvalue problems. Oberwolfach Rep., 10(4):3296-3298, 2013.
bib | DOI ]
[5] A. Uschmajew. The regularity of tensor product approximations in L² in dependence of the target function. Oberwolfach Rep., 8(2):1802-1804, 2011.
bib | DOI ]

Thesis:

[1] A. Uschmajew. Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen. PhD thesis, Technische Universität Berlin, Jan. 2013.
bib | http ]