Prof. Dr. André Uschmajew

Chair
Mathematical Data Science
Phone: +49 821 598 2033
Email: andre.uschmajew@uni-a.de
Room: 3038 (L1)
Visiting hours: by appointment
Address: Universitätsstraße 14, 86159 Augsburg

Curriculum Vitae

2022 -              Chair of Mathematical Data Science, University of Augsburg

2019, 2020      Visiting professor, Leipzig University

2017 - 2022     Research group leader, Max Planck Institute MiS Leipzig

2014 - 2017     Bonn Junior Fellow professorship, University of Bonn

2013 - 2014     Research associate, EPF Lausanne

2013                Dissertation in Mathematics, TU Berlin

2008 - 2013     Research associate, TU Berlin

2008                Diploma in Mathematics, TU Berlin

Research Topics

  • Tensors: geometry of low-rank varieties and tensor networks tensor product operators
  • Low-rank approximation: functional analytic foundations, approximation rates, spectral and nuclear norm
  • Optimization: block coordinate methods, Riemannian optimization, optimization landscape of multilinear models
  • Applications: high-dimensional problems, low-rank models in data science, signal processing, dynamical low-rank approximation

Publications

Publication list at Google Scholar
 

Journal articles, book chapters, proceedings

Ivan V. Oseledets, Maxim V. Rakhuba and André Uschmajew
Local convergence of alternating low‐rank optimization methods with overrelaxation

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Henrik Eisenmann and André Uschmajew
Maximum relative distance between real rank-two and rank-one tensors

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Henrik Eisenmann, Felix Krahmer, Max Pfeffer and André Uschmajew
Riemannian thresholding methods for row-sparse and low-rank matrix recovery

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Tobias Lehmann, Max-K. von Renesse, Alexander Sambale and André Uschmajew
A note on overrelaxation in the Sinkhorn algorithm

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André Uschmajew and Bart Vandereycken
A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions

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Edoardo Di Napoli, Paolo Bientinesi, Jiajia Li and André Uschmajew
Editorial: high-performance tensor computations in scientific computing and data science

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Christian Krumnow, Max Pfeffer and André Uschmajew
Computing eigenspaces with low rank constraints

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André Uschmajew, M. Bachmayr, H. Eisenmann and E. Kieri
Dynamical low-rank approximation for parabolic problems

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In: Mini-Workshop: Computational Optimization on Manifolds

Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew
Existence of dynamical low-rank approximations to parabolic problems

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Wolfgang Hackbusch and André Uschmajew
Modified iterations for data-sparse solution of linear systems

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Andrei Agrachev, Khazhgali Kozhasov and André Uschmajew
Chebyshev polynomials and best rank-one approximation ratio

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André Uschmajew and Bart Vandereycken
Geometric methods on low-rank matrix and tensor manifolds

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André Uschmajew and Bart Vandereycken
On critical points of quadratic low-rank matrix optimization problems

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Anh-Huy Phan, Andrzej Cichocki, André Uschmajew, Petr Tichavsky, George Luta and Danilo P. Mandic
Tensor networks for latent variable analysis: novel algorithms for tensor train approximation

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Seyedehsomayeh Hosseini and André Uschmajew
A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization

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Max Pfeffer, André Uschmajew, Adriana Amaro and Ulrich Pfeffer
Data fusion techniques for the integration of multi-domain genomic data from uveal melanoma

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Seyedehsomayeh Hosseini, D. Russell Luke and André Uschmajew
Tangent and normal cones for low-rank matrices

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Ivan V. Oseledets, Maxim V. Rakhuba and André Uschmajew
Alternating least squares as moving subspace correction

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Zhening Li, Yuji Nakatsukasa, Tasuku Soma and André Uschmajew
On orthogonal tensors and best rank-one approximation ratio

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Seyedehsomayeh Hosseini and André Uschmajew
A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds

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Yuji Nakatsukasa, Tasuku Soma and André Uschmajew
Finding a low-rank basis in a matrix subspace

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Wolfgang Hackbusch and André Uschmajew
On the interconnection between the higher-order singular values of real tensors

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Wolfgang Hackbusch, Daniel Kressner and André Uschmajew
Perturbation of higher-order singular values

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Daniel Kressner and André Uschmajew
On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

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Lars Karlsson, Daniel Kressner and André Uschmajew
Parallel algorithms for tensor completion in the CP format

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Markus Bachmayr, Reinhold Schneider and André Uschmajew
Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations

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André Uschmajew
A new convergence proof for the higher-order power method and generalizations

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Reinhold Schneider and André Uschmajew
Convergence results for projected line-search methods on varieties of low-rank matrices via Łojasiewicz inequality

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André Uschmajew and Bart Vandereycken
Greedy rank updates combined with Riemannian descent methods for low-rank optimization

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Zhening Li, André Uschmajew and Shuzhong Zhang
On convergence of the maximum block improvement method

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André Uschmajew
Some results concerning rank-one truncated steepest descent directions in tensor spaces

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Reinhold Schneider and André Uschmajew
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces

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André Uschmajew and Bart Vandereycken
Line-search methods and rank increase on low-rank matrix varieties

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Daniel Kressner, Michael Steinlechner and André Uschmajew
Low-rank tensor methods with subspace correction for symmetric eigenvalue problems

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André Uschmajew, D. Kressner and M. Steinlechner
Low-rank tensor methods with subspace correction for symmetric eigenvalue problems

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In: Numerical solution of PDE eigenvalue problems, 17 November - 23 November 2013; report no. 56/2013

Thorsten Rohwedder and André Uschmajew
On local convergence of alternating schemes for optimization of convex problems in the tensor train format

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André Uschmajew and Bart Vandereycken
The geometry of algorithms using hierarchical tensors

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Sambasiva Rao Chinnamsetty, Hongjun Luo, Wolfgang Hackbusch, Heinz-Jürgen Flad and André Uschmajew
Bridging the gap between quantum Monte Carlo and F12-methods

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André Uschmajew
Local convergence of the alternating least squares algorithm for canonical tensor approximation

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André Uschmajew
Regularity of tensor product approximations to square integrable functions

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André Uschmajew
The regularity of tensor product approximations in L2 in dependence of the target function

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In: Mathematical methods in quantum chemistry, June 26th - July 2nd, 2011, report no. 32/2011

André Uschmajew
Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations

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Dissertation

André Uschmajew
Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen

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Dissertation, TU Berlin, 2013

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