Tensors and Optimization
Head:
André Uschmajew (Email)
Phone:
+49 (0) 341 - 9959 - 824
Fax:
+49 (0) 341 - 9959 - 658
Address:
Inselstr. 22
04103 Leipzig
Institute publications of the group
Preprints
M. Dressler ; A. Uschmajew and V. Chandrasekaran:
Kronecker product approximation of operators in spectral norm via alternating SDP.
Bibtex MIS-Preprint: 21/2022 [ARXIV] Repository Open Access
A. Bernardi ; C. De Lazzari and F. Gesmundo:
Dimension of tensor network varieties.
Bibtex MIS-Preprint: 1/2021 [ARXIV] Repository Open Access
P. Breiding ; F. Gesmundo ; M. Michałek and N. Vannieuwenhoven:
Algebraic compressed sensing.
Bibtex [ARXIV] Repository Open Access
M. Pfeffer and J. A.
Samper:
The cone of \(5\times 5\) completely positive matrices.
Bibtex [ARXIV] Repository Open Access
Books
S. Hosseini ; B. S. Mordukhovich and A. Uschmajew (eds.):
Nonsmooth optimization and its applications : based on the workshop 'Nonsmooth optimization
and its Applications', Bonn, Germany, May 15-19, 2017.
Springer Birkhäuser, 2019. - VII, 149 p.
(International series of numerical mathematics ; 170)
ISBN 978-3-030-11369-8 Bibtex [DOI]
S. Dahlke ; W. Dahmen ; M. Griebel ; W. Hackbusch ; K. Ritter ; R. Schneider ; C. Schwab and H. Yserentant (eds.):
Extraction of quantifiable information from complex systems.
Springer, 2014. - XIX, 432 p.
(Lecture notes in computational science and engineering ; 102)
ISBN 978-3-319-08158-8 Bibtex [DOI]
Journal articles and proceedings
A. Bik and H. Eisenmann:
The geometries of Jordan nets and Jordan webs.
Annali di matematica pura ed applicata,
201 (2022) 5, p. 2413-2464 Bibtex MIS-Preprint: 1/2022 [DOI] [ARXIV] [CODELINK] Journal Open Access
A. Conner ; F. Gesmundo ; J. M. Landsberg and E. Ventura:
Rank and border rank of Kronecker powers of tensors and Strassen's laser method.
Computational complexity,
31 (2022) 1, 1 Bibtex [DOI] [ARXIV] Journal Open Access
E. Di Napoli ; P. Bientinesi ; J. Li and A. Uschmajew:
Editorial : High-performance tensor computations in scientific computing and data
science.
Frontiers in applied mathematics and statistics,
Vol. not yet known, pp. not yet known Bibtex [DOI] Journal Open Access
H. Eisenmann ; F. Krahmer ; M. Pfeffer and A. Uschmajew:
Riemannian thresholding methods for row-sparse and low-rank matrix recovery.
Numerical algorithms,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 4/2021 [DOI] [ARXIV] Journal Open Access
H. Eisenmann and Y. Nakatsukasa:
Solving two-parameter eigenvalue problems using an alternating method.
Linear algebra and its applications,
643 (2022), p. 137-160 Bibtex MIS-Preprint: 83/2020 [DOI] [ARXIV] [CODELINK] Journal Open Access
H. Eisenmann and A. Uschmajew:
Maximum relative distance between real rank-two and rank-one tensors.
Annali di matematica pura ed applicata,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 27/2021 [DOI] [ARXIV] Journal Open Access
F. Gesmundo and C. Meroni:
The geometry of discotopes.
Le Matematiche,
77 (2022) 1, p. 143-171 Bibtex [ARXIV] [FREELINK] Journal Open Access
T. Lehmann ; M. v.
Renesse ; A. Sambale and A. Uschmajew:
A note on overrelaxation in the Sinkhorn algorithm.
Optimization letters,
16 (2022) 8, p. 2209-2220 Bibtex MIS-Preprint: 110/2020 [DOI] [ARXIV] Journal Open Access
I. V. Oseledets ; M. Rakhuba and A. Uschmajew:
Local convergence of alternating low-rank optimization methods with overrelaxation.
Numerical linear algebra with applications,
Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 29/2021 [DOI] [ARXIV] Repository Open Access
A. Uschmajew and B. 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 (2022) 1, p. 364-373 Bibtex MIS-Preprint: 17/2021 [DOI] [ARXIV] Journal Open Access
M. Bachmayr ; H. Eisenmann ; E. Kieri and A. Uschmajew:
Existence of dynamical low-rank approximations to parabolic problems.
Mathematics of computation,
90 (2021) 330, p. 1799-1830 Bibtex MIS-Preprint: 33/2020 [DOI] [ARXIV] Repository Open Access
A. Bik ; H. Eisenmann and B. Sturmfels:
Jordan algebras of symmetric matrices.
Le Matematiche,
76 (2021) 2, p. 337-353 Bibtex [DOI] [ARXIV] [CODELINK] Journal Open Access
T. Brysiewicz and F. Gesmundo:
The degree of Stiefel manifolds.
Enumerative combinatorics and applications,
1 (2021) 3, S2R20 Bibtex [DOI] [ARXIV] Journal Open Access
M. Christandl ; F. Gesmundo ; M. Michałek and J. Zuiddam:
Border rank non-additivity for higher order tensors.
SIAM journal on matrix analysis and applications,
42 (2021) 2, p. 503-527 Bibtex [DOI] [ARXIV] Repository Open Access
M. Christandl ; F. Gesmundo ; D. Stilck França and A. H. Werner:
Optimization at the boundary of the tensor network variety.
Physical review / B,
103 (2021) 9, 195139 Bibtex [DOI] [ARXIV] Repository Open Access
W. Hackbusch and A. Uschmajew:
Modified iterations for data-sparse solution of linear systems.
Vietnam journal of mathematics,
49 (2021) 2, p. 493-512 Bibtex MIS-Preprint: 58/2020 [DOI] Journal Open Access
C. Krumnow ; M. Pfeffer and A. Uschmajew:
Computing eigenspaces with low rank constraints.
SIAM journal on scientific computing,
43 (2021) 1, p. A586-A608 Bibtex MIS-Preprint: 102/2019 [DOI] Repository Open Access
A. Agrachev ; K. Kozhasov and A. Uschmajew:
Chebyshev polynomials and best rank-one approximation ratio.
SIAM journal on matrix analysis and applications,
41 (2020) 1, p. 308-331 Bibtex MIS-Preprint: 34/2019 [DOI] [ARXIV] [PDF] Repository Open Access
M. Eigel ; M. Marschall ; M. Pfeffer and R. Schneider:
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor
representations.
Numerische Mathematik,
145 (2020) 3, p. 655-692 Bibtex MIS-Preprint: 47/2018 [DOI] [ARXIV] Journal Open Access
A.-H. Phan ; A. Cichocki ; A. Uschmajew ; P. Tichavsky ; G. Luta and D. Mandic:
Tensor networks for latent variable analysis : novel algorithms for tensor train approximation.
IEEE transactions on neural networks and learning systems,
31 (2020) 11, p. 4622-4636 Bibtex [DOI] [ARXIV] Repository Open Access
A. Uschmajew ; M. Bachmayr ; H. Eisenmann and E. Kieri:
Dynamical low-rank approximation for parabolic problems [In: Mini-workshop : computational
optimization on manifolds ; 15 November - 21 November 2020 ; report no. 36/2020].
Oberwolfach reports,
17 (2020) 4, p. 1800-1802 Bibtex [DOI] [FREELINK] Repository Open Access
A. Uschmajew and B. Vandereycken:
On critical points of quadratic low-rank matrix optimization problems.
IMA journal of numerical analysis,
40 (2020) 4, p. 2626-2651 Bibtex MIS-Preprint: 58/2018 [DOI] Journal Open Access
A. Uschmajew and B. Vandereycken:
Geometric methods on low-rank matrix and tensor manifolds.
Handbook of variational methods for nonlinear geometric data / P.
Grohs... (eds.). Springer, 2020. - P. 261-313 Bibtex [DOI] [PDF] Journal Open Access
S. Hosseini ; D. R.
Luke and A. Uschmajew:
Tangent and normal cones for low-rank matrices.
Nonsmooth optimization and its applications : based on the workshop 'Nonsmooth optimization
and its Applications', Bonn, Germany, May 15-19, 2017 / S.
Hosseini... (eds.). Springer Birkhäuser, 2019. - P. 45-53
(International series of numerical mathematics ; 170)
Bibtex [DOI] [FREELINK] Repository Open Access
S. Hosseini and A. Uschmajew:
A gradient sampling method on algebraic varieties and application to nonsmooth low-rank
optimization.
SIAM journal on optimization,
29 (2019) 4, p. 2853-2880 Bibtex [DOI] [PDF] Repository Open Access
M. Pfeffer ; A. Seigal and B. Sturmfels:
Learning paths from signature tensors.
SIAM journal on matrix analysis and applications,
40 (2019) 2, p. 394-416 Bibtex MIS-Preprint: 78/2018 [DOI] [ARXIV] Repository Open Access
M. Pfeffer ; A. Uschmajew ; A. Amaro and U. Pfeffer:
Data fusion techniques for the integration of multi-domain genomic data from uveal
melanoma.
Cancers,
11 (2019) 10, 1434 Bibtex MIS-Preprint: 42/2019 [DOI] Journal Open Access
Z. Li ; Y. Nakatsukasa ; T. Soma and A. Uschmajew:
On orthogonal tensors and best rank-one approximation ratio.
SIAM journal on matrix analysis and applications,
39 (2018) 1, p. 400-425 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
I. V. Oseledets ; M. Rakhuba and A. Uschmajew:
Alternating least squares as moving subspace correction.
SIAM journal on numerical analysis,
56 (2018) 6, p. 3459-3479 Bibtex [DOI] [ARXIV] [PDF] Repository Open Access
W. Hackbusch ; D. Kressner and A. Uschmajew:
Perturbation of higher-order singular values.
SIAM journal on applied algebra and geometry,
1 (2017) 1, p. 374-387 Bibtex MIS-Preprint: 51/2016 [DOI] [PDF] Journal Open Access
W. Hackbusch and A. Uschmajew:
On the interconnection between the higher-order singular values of real tensors.
Numerische Mathematik,
135 (2017) 3, p. 875-894 Bibtex MIS-Preprint: 62/2015 [DOI] Journal Open Access
S. Dahlke ; W. Dahmen ; M. Griebel ; W. Hackbusch ; K. Ritter ; R. Schneider ; C. Schwab and H. Yserentant:
Foreword.
Extraction of quantifiable information from complex systems / S.
Dahlke... (eds.). Springer, 2014
(Lecture notes in computational science and engineering ; 102)
Bibtex [DOI]
W. Hackbusch and R. Schneider:
Tensor spaces and hierarchical tensor representations.
Extraction of quantifiable information from complex systems / S.
Dahlke... (eds.). Springer, 2014. - P. 237-261
(Lecture notes in computational science and engineering ; 102)
Bibtex [DOI]
S. R.
Chinnamsetty ; H. Luo ; W. Hackbusch ; H.-J. Flad and A. Uschmajew:
Bridging the gap between quantum Monte Carlo and F12-methods.
Chemical physics,
401 (2012), p. 36-44 Bibtex MIS-Preprint: 68/2011 [DOI] [PDF] Repository Open Access
H.-J. Flad ; W. Hackbusch ; D. Kolb and R. Schneider:
Wavelet approximation of correlated wave functions. I. Basics.
The journal of chemical physics,
116 (2002) 22, p. 9641-9657 Bibtex MIS-Preprint: 89/2001 [DOI] Repository Open Access
Thesis
H. Eisenmann:
Multilinear optimization in low-rank models.
Dissertation, Universität Leipzig, 2022 Bibtex [FREELINK]
