

2013  Dr. rer. nat., TU Berlin  2013  2014  Postdoc, École polytechnique fédérale de Lausanne (EPFL), Switzerland  Since 2014  Professor (W2, Bonn Junior Fellow), University of Bonn 


My research is on different aspects of lowrank tensor decomposition and approximation, that is, on multilinear and datasparse representations of highdimensional objects. For example, one may think of large arrays of numbers arising from data acquisition or the discretization of a multivariate functions. Lowrank tensor approximation aims at generalizing lowrank matrix approximation, which turns out to be a highly nontrivial task. This relatively new field of numerical mathematics connects to other branches of mathematics, such as approximation theory, algebraic/differential geometry, and nonlinear optimization. Its areas of application include highdimensional partial differential equations, statistics, signal processing and (big) data analysis. It hence offers research possibilities in several directions. For example, in scientific computing, lowrank tensor techniques make it possible to treat some problems of very high dimension for which classical discretization schemes are unmanageable. In data analysis and signal processing, lowrank methods are used for identification of principal components and hidden sources. Personally, I have worked on the convergence analysis of nonlinear lowrank tensor optimization methods, as well as on more fundamental questions regarding lowrank approximability of functions and solutions to tensor structured equations.
Accordingly, the future research aims at the derivation of novel theoretical methods and concepts to acquire a more fundamental understanding of the mechanisms that make lowrank tensor approximation possible. This is important for identifying the problem classes for which these techniques can be successfully applied. The theoretical investigations go hand in hand with the design and analysis of innovative computational methods for dealing with problems that require the processing or approximation of higherorder tensors and multivariate functions.


[ 1] Markus Bachmayr, Reinhold Schneider, André Uschmajew
Tensor networks and hierarchical tensors for the solution of highdimensional partial differential equations Found. Comput. Math. , 16: (6): 14231472 2016 DOI: 10.1007/s1020801693179[ 2] Reinhold Schneider, André Uschmajew
Convergence results for projected linesearch methods on varieties of lowrank matrices via \L ojasiewicz inequality SIAM J. Optim. , 25: (1): 622646 2015 DOI: 10.1137/140957822[ 3] André Uschmajew
A new convergence proof for the higherorder power method and generalizations Pac. J. Optim. , 11: (2): 309321 2015[ 4] Daniel Kressner, Michael Steinlechner, André Uschmajew
Lowrank tensor methods with subspace correction for symmetric eigenvalue problems SIAM J. Sci. Comput. , 36: (5): A2346A2368 2014 DOI: 10.1137/130949919[ 5] Reinhold Schneider, André Uschmajew
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces J. Complexity , 30: (2): 5671 2014 DOI: 10.1016/j.jco.2013.10.001[ 6] Thorsten Rohwedder, André Uschmajew
On local convergence of alternating schemes for optimization of convex problems in the tensor train format SIAM J. Numer. Anal. , 51: (2): 11341162 2013 DOI: 10.1137/110857520[ 7] André Uschmajew, Bart Vandereycken
The geometry of algorithms using hierarchical tensors Linear Algebra Appl. , 439: (1): 133166 2013 DOI: 10.1016/j.laa.2013.03.016[ 8] André Uschmajew
Local convergence of the alternating least squares algorithm for canonical tensor approximation SIAM J. Matrix Anal. Appl. , 33: (2): 639652 2012 DOI: 10.1137/110843587[ 9] André Uschmajew
Regularity of tensor product approximations to square integrable functions Constr. Approx. , 34: (3): 371391 2011 DOI: 10.1007/s0036501091254[ 10] André Uschmajew
Wellposedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations Numer. Math. , 115: (2): 309331 2010 DOI: 10.1007/s0021100902769



2013  16th IMA Leslie Fox Prize in Numerical Analysis (second place)  2013  2013 Tiburtius Prize of the Berlin universities (second place) 


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