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Former Research Group

Tensors and Optimization

The research in our group focused on low-rank matrix and tensor approximation, with emphasis on numerical tensor calculus, nonlinear optimization methods, underlying approximability principles, as well as algebraic and geometric foundations. Our goal was to obtain a deeper understanding of low-rank models and methods, and their successful use in scientific computing and modern applications. Some keywords:

  • Tensors: geometry of low-rank varieties, tensor networks, higher-order singular values, tensor product operators

  • Approximation: functional analytic foundations, approximation rates, singular value estimates, spectral and nuclear norm

  • Optimization: block coordinate methods, truncated iterations, Riemannian optimization, rank adaptivity, optimization landscape

  • Applications: high-dimensional linear equations and eigenvalue problems, signal processing, dynamical low-rank approximation

André Uschmajew

Universität Augsburg
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Publications

inJournal
2023
Paul Breiding et al.

Algebraic compressed sensing

In: Applied and computational harmonic analysis
BibTex DOI: 10.1016/j.acha.2023.03.006 ArXiv: 2108.13208
inJournal
2023
Alessandra Bernardi et al.

Dimension of tensor network varieties

In: Communications in contemporary mathematics
BibTex DOI: 10.1142/S0219199722500596 ArXiv: 2101.03148 MiS Preprint
inJournal
2023
Mareike Dressler et al.

Kronecker product approximation of operators in spectral norm via alternating SDP

In: SIAM journal on matrix analysis and applications
BibTex DOI: 10.1137/22M1509953 ArXiv: 2207.03186 MiS Preprint
inJournal
2023
Ivan V. Oseledets et al.

Local convergence of alternating low-rank optimization methods with overrelaxation

In: Numerical linear algebra with applications
BibTex DOI: 10.1002/nla.2459 ArXiv: 2111.14758 MiS Preprint
inJournal
2023
Henrik Eisenmann et al.

Maximum relative distance between real rank-two and rank-one tensors

In: Annali di matematica pura ed applicata
BibTex DOI: 10.1007/s10231-022-01268-w ArXiv: 2111.12611 MiS Preprint
inJournal
2023
Henrik Eisenmann et al.

Riemannian thresholding methods for row-sparse and low-rank matrix recovery

In: Numerical algorithms
BibTex DOI: 10.1007/s11075-022-01433-5 ArXiv: 2103.02356 MiS Preprint
inJournal
2022
Tobias Lehmann et al.

A note on overrelaxation in the Sinkhorn algorithm

In: Optimization letters
BibTex DOI: 10.1007/s11590-021-01830-0 ArXiv: 2012.12562 MiS Preprint
inJournal
2022
André Uschmajew et al.

A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions

In: Journal of optimization theory and applications
BibTex DOI: 10.1007/s10957-022-02032-z ArXiv: 2106.08020 MiS Preprint
inJournal
2022
Edoardo Di Napoli et al.

Editorial : High-performance tensor computations in scientific computing and data science

In: Frontiers in applied mathematics and statistics
BibTex DOI: 10.3389/fams.2022.1038885
Academic
2022
Henrik Eisenmann

Multilinear optimization in low-rank models

Dissertation, Universität Leipzig
BibTex Link: nbn-resolving.org
inJournal
2022
Austin Conner et al.

Rank and border rank of Kronecker powers of tensors and Strassen's laser method

In: Computational complexity
BibTex DOI: 10.1007/s00037-021-00217-y ArXiv: 1909.04785
inJournal
2022
Henrik Eisenmann et al.

Solving two-parameter eigenvalue problems using an alternating method

In: Linear algebra and its applications
BibTex DOI: 10.1016/j.laa.2022.02.024 ArXiv: 2008.03385 MiS Preprint Code: mathrepo.mis.mpg.de
inJournal
2022
Arthur Bik et al.

The geometries of Jordan nets and Jordan webs

In: Annali di matematica pura ed applicata
BibTex DOI: 10.1007/s10231-022-01204-y ArXiv: 2201.04403 MiS Preprint Code: mathrepo.mis.mpg.de
inJournal
2022
Fulvio Gesmundo et al.

The geometry of discotopes

In: Le Matematiche
BibTex ArXiv: 2111.01241 Link: lematematiche.dmi.unict.it
inJournal
2021
Max von Renesse et al.

On overrelaxation in the Sinkhorn algorithm [In: Applications of optimal transportation in the natural sciences ; 21 February - 27 February 2021 ; report no. 10/2021]

In: Oberwolfach reports
DOI: 10.4171/OWR/2021/10 Link: publications.mfo.de
inJournal
2021
Matthias Christandl et al.

Border rank non-additivity for higher order tensors

In: SIAM journal on matrix analysis and applications
BibTex DOI: 10.1137/20M1357366 ArXiv: 2007.05458
inJournal
2021
Christian Krumnow et al.

Computing eigenspaces with low rank constraints

In: SIAM journal on scientific computing
BibTex DOI: 10.1137/19M1308384 MiS Preprint
inJournal
2021
Markus Bachmayr et al.

Existence of dynamical low-rank approximations to parabolic problems

In: Mathematics of computation
BibTex DOI: 10.1090/mcom/3626 ArXiv: 2002.12197 MiS Preprint
inJournal
2021
Arthur Bik et al.

Jordan algebras of symmetric matrices

In: Le Matematiche
BibTex DOI: 10.4418/2021.76.2.3 ArXiv: 2010.00277 Code: mathrepo.mis.mpg.de
inJournal
2021
Wolfgang Hackbusch et al.

Modified iterations for data-sparse solution of linear systems

In: Vietnam journal of mathematics
BibTex DOI: 10.1007/s10013-021-00504-9 MiS Preprint
All Group Publications
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