Prof. Dr. André Uschmajew

Chair
Mathematical Data Science
Phone: +49 821 598 2033
Email:
Room: 3038 (L1)
Open 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
 

Preprints

Markus Bachmayr, Henrik Eisenmann and André Uschmajew
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
arXiv:2308.16720 (2023)

 

Guillaume Olikier, André Uschmajew and Bart Vandereycken
Gauss-Southwell type descent methods for low-rank matrix optimization
arXiv:2306.00897 (2023)

 

Daniel Kressner, Tingting Ni and André Uschmajew
On the approximation of vector-valued functions by samples
arXiv:2304.03212 (2023)

 

André Uschmajew and Andreas Zeiser
Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary
arXiv:2303.01856 (2023)

 

Journal articles, book chapters, proceedings

Daniel Kressner, Tingting Ni and André Uschmajew
On the approximation of vector-valued functions by volume sampling

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Antonio Bellon, Mareike Dressler, Vyacheslav Kungurtsev, Jakub Marecek and André Uschmajew
Time-varying semidefinite programming: path following a Burer-Monteiro factorization

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Mareike Dressler, André Uschmajew and Venkat Chandrasekaran
Kronecker product approximation of operators in spectral norm via alternating SDP

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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

BibTeX | RIS | DOI

Dissertation, TU Berlin, 2013

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