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Markus Bachmayr, Henrik Eisenmann and André Uschmajew
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
Numerische Mathematik , (in print)
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Guillaume Olikier, André Uschmajew and Bart Vandereycken
Gauss–Southwell type descent methods for low-rank matrix optimization
Journal of Optimization Theory and Applications 206, 6 (2025)
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Daniel Kressner, Tingting Ni and André Uschmajew
On the approximation of vector-valued functions by volume sampling
Journal of Complexity 86, 101887 (2025)
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André Uschmajew and Andreas Zeiser
Dynamical low-rank approximation of the Vlasov–Poisson equation with piecewise linear spatial boundary
BIT Numerical Mathematics 64, 19 (2024)
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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
SIAM Journal on Optimization 34, 1-26 (2024)
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Mareike Dressler, André Uschmajew and Venkat Chandrasekaran
Kronecker product approximation of operators in spectral norm via alternating SDP
SIAM Journal on Matrix Analysis and Applications 44, 1693-1708 (2023)
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Ivan V. Oseledets, Maxim V. Rakhuba and André Uschmajew
Local convergence of alternating low‐rank optimization methods with overrelaxation
Numerical Linear Algebra with Applications 30, e2459 (2023)
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Henrik Eisenmann and André Uschmajew
Maximum relative distance between real rank-two and rank-one tensors
Annali di Matematica Pura ed Applicata 202, 993-1009 (2023)
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Henrik Eisenmann, Felix Krahmer, Max Pfeffer and André Uschmajew
Riemannian thresholding methods for row-sparse and low-rank matrix recovery
Numerical Algorithms 93, 669-693 (2023)
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Tobias Lehmann, Max-K. von Renesse, Alexander Sambale and André Uschmajew
A note on overrelaxation in the Sinkhorn algorithm
Optimization Letters 16, 2209-2220 (2022)
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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
Journal of Optimization Theory and Applications 194, 364-373 (2022)
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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
Frontiers in Applied Mathematics and Statistics 8, 1038885 (2022)
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Christian Krumnow, Max Pfeffer and André Uschmajew
Computing eigenspaces with low rank constraints
SIAM Journal on Scientific Computing 43, A586-A608 (2021)
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André Uschmajew, M. Bachmayr, H. Eisenmann and E. Kieri
Dynamical low-rank approximation for parabolic problems
Oberwolfach Reports 17, 1800-1802 (2021)
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In: Mini-Workshop: Computational Optimization on Manifolds
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Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew
Existence of dynamical low-rank approximations to parabolic problems
Mathematics of Computation 90, 1799-1830 (2021)
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Wolfgang Hackbusch and André Uschmajew
Modified iterations for data-sparse solution of linear systems
Vietnam Journal of Mathematics 49, 493-512 (2021)
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Andrei Agrachev, Khazhgali Kozhasov and André Uschmajew
Chebyshev polynomials and best rank-one approximation ratio
SIAM Journal on Matrix Analysis and Applications 41, 308-331 (2020)
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André Uschmajew and Bart Vandereycken
Geometric methods on low-rank matrix and tensor manifolds
in: Handbook of variational methods for nonlinear geometric data, ed. by Philipp Grohs, Martin Holler and Andreas Weinmann, 261-313 (Springer: Cham, 2020)
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André Uschmajew and Bart Vandereycken
On critical points of quadratic low-rank matrix optimization problems
IMA Journal of Numerical Analysis 40, 2626-2651 (2020)
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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
IEEE Transactions on Neural Networks and Learning Systems 31, 4622-4636 (2020)
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Seyedehsomayeh Hosseini and André Uschmajew
A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization
SIAM Journal on Optimization 29, 2853-2880 (2019)
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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
Cancers 11, 1434 (2019)
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Seyedehsomayeh Hosseini, D. Russell Luke and André Uschmajew
Tangent and normal cones for low-rank matrices
in: Nonsmooth optimization and its applications, ed. by Seyedehsomayeh Hosseini, Boris S. Mordukhovich and André Uschmajew, (International Series of Numerical Mathematics ; 170) 45-53 (Springer: Cham, 2019)
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Ivan V. Oseledets, Maxim V. Rakhuba and André Uschmajew
Alternating least squares as moving subspace correction
SIAM Journal on Numerical Analysis 56, 3459-3479 (2018)
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Zhening Li, Yuji Nakatsukasa, Tasuku Soma and André Uschmajew
On orthogonal tensors and best rank-one approximation ratio
SIAM Journal on Matrix Analysis and Applications 39, 400-425 (2018)
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Seyedehsomayeh Hosseini and André Uschmajew
A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds
SIAM Journal on Optimization 27, 173-189 (2017)
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Yuji Nakatsukasa, Tasuku Soma and André Uschmajew
Finding a low-rank basis in a matrix subspace
Mathematical Programming 162, 325-361 (2017)
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Wolfgang Hackbusch and André Uschmajew
On the interconnection between the higher-order singular values of real tensors
Numerische Mathematik 135, 875-894 (2017)
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Wolfgang Hackbusch, Daniel Kressner and André Uschmajew
Perturbation of higher-order singular values
SIAM Journal on Applied Algebra and Geometry 1, 374-387 (2017)
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Daniel Kressner and André Uschmajew
On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems
Linear Algebra and its Applications 493, 556-572 (2016)
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Lars Karlsson, Daniel Kressner and André Uschmajew
Parallel algorithms for tensor completion in the CP format
Parallel Computing 57, 222-234 (2016)
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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
Foundations of Computational Mathematics 16, 1423-1472 (2016)
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André Uschmajew
A new convergence proof for the higher-order power method and generalizations
Pacific Journal of Optimization 11, 309-321 (2015)
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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
SIAM Journal on Optimization 25, 622-646 (2015)
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André Uschmajew and Bart Vandereycken
Greedy rank updates combined with Riemannian descent methods for low-rank optimization
in: 2015 International Conference on Sampling Theory and Applications (SampTA), 25-29 May 2015, Washington, DC, USA, ed. by Stephen Casey, Kevin Duke, Michael Robinson, 420-424 (IEEE: Piscataway, NJ, 2015)
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Zhening Li, André Uschmajew and Shuzhong Zhang
On convergence of the maximum block improvement method
SIAM Journal on Optimization 25, 210-233 (2015)
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André Uschmajew
Some results concerning rank-one truncated steepest descent directions in tensor spaces
in: 2015 International Conference on Sampling Theory and Applications (SampTA), 25-29 May 2015, Washington, DC, USA, ed. by Stephen Casey, Kevin Duke, Michael Robinson, 415-419 (IEEE: Piscataway, NJ, 2015)
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Reinhold Schneider and André Uschmajew
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces
Journal of Complexity 30, 56-71 (2014)
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André Uschmajew and Bart Vandereycken
Line-search methods and rank increase on low-rank matrix varieties
in: 2014 International Symposium on Nonlinear Theory and its Applications (NOLTA2014), Luzern, Switzerland, September 14-18, 2014, 52-55 (IEICE: Luzern, 2014)
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Daniel Kressner, Michael Steinlechner and André Uschmajew
Low-rank tensor methods with subspace correction for symmetric eigenvalue problems
SIAM Journal on Scientific Computing 36, A2346-A2368 (2014)
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André Uschmajew, D. Kressner and M. Steinlechner
Low-rank tensor methods with subspace correction for symmetric eigenvalue problems
Oberwolfach Reports 10, 3296-3298 (2013)
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In: Numerical solution of PDE eigenvalue problems, 17 November - 23 November 2013; report no. 56/2013
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Thorsten Rohwedder and André Uschmajew
On local convergence of alternating schemes for optimization of convex problems in the tensor train format
SIAM Journal on Numerical Analysis 51, 1134-1162 (2013)
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André Uschmajew and Bart Vandereycken
The geometry of algorithms using hierarchical tensors
Linear Algebra and its Applications 439, 133-166 (2013)
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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
Chemical Physics 401, 36-44 (2012)
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André Uschmajew
Local convergence of the alternating least squares algorithm for canonical tensor approximation
SIAM Journal on Matrix Analysis and Applications 33, 639-652 (2012)
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André Uschmajew
Regularity of tensor product approximations to square integrable functions
Constructive Approximation 34, 371-391 (2011)
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André Uschmajew
The regularity of tensor product approximations in L2 in dependence of the target function
Oberwolfach Reports 8, 1802-1804 (2011)
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In: Mathematical methods in quantum chemistry, June 26th - July 2nd, 2011, report no. 32/2011
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André Uschmajew
Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations
Numerische Mathematik 115, 309-331 (2010)
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