Profile
Profile

Prof. Dr. André Uschmajew

Bonn Junior Fellow

E-mail: uschmajew(at)ins.uni-bonn.de
Phone: +49 228 73 4091
Homepage: http://uschmajew.ins.uni-bonn.de/people/uschmajew.html
Room: 6.019
Location: Computing Center
Institute: Institute for Numerical Simulation
Research Areas: Research Area B
Research Area J

Academic Career

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

Research Profile

My research is on different aspects of low-rank tensor decomposition and approximation, that is, on multilinear and data-sparse representations of high-dimensional objects. For example, one may think of large arrays of numbers arising from data acquisition or the discretization of a multivariate functions. Low-rank tensor approximation aims at generalizing low-rank 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 high-dimensional partial differential equations, statistics, signal processing and (big) data analysis. It hence offers research possibilities in several directions. For example, in scientific computing, low-rank 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, low-rank methods are used for identification of principal components and hidden sources. Personally, I have worked on the convergence analysis of nonlinear low-rank tensor optimization methods, as well as on more fundamental questions regarding low-rank 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 low-rank 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 higher-order tensors and multivariate functions.

Selected Publications

[1] Markus Bachmayr, Reinhold Schneider, André Uschmajew
Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations
Found. Comput. Math. , 16: (6): 1423--1472
2016
ISSN: 1615-3375
DOI: 10.1007/s10208-016-9317-9

Publication List

Awards

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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