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
Research Group Leader
30.09.17
30.09.22
André Uschmajew
Universität Augsburg
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Publications
inJournal
2023Dimension of tensor network varieties
In: Communications in contemporary mathematicsinJournal
2023Algebraic compressed sensing
In: Applied and computational harmonic analysisPreprint
2023Quatroids and rational plane cubics
inJournal
2023Kronecker product approximation of operators in spectral norm via alternating SDP
In: SIAM journal on matrix analysis and applicationsinJournal
2023Maximum relative distance between real rank-two and rank-one tensors
In: Annali di matematica pura ed applicatainJournal
2023Riemannian thresholding methods for row-sparse and low-rank matrix recovery
In: Numerical algorithmsPreprint
2023Hilbert functions of chopped ideals
inJournal
2023Local convergence of alternating low-rank optimization methods with overrelaxation
In: Numerical linear algebra with applicationsinJournal
2022The geometries of Jordan nets and Jordan webs
In: Annali di matematica pura ed applicatainJournal
2022Rank and border rank of Kronecker powers of tensors and Strassen's laser method
In: Computational complexityinJournal
2022Editorial : High-performance tensor computations in scientific computing and data science
In: Frontiers in applied mathematics and statisticsAcademic
2022Multilinear optimization in low-rank models
Dissertation, Universität LeipziginJournal
2022Solving two-parameter eigenvalue problems using an alternating method
In: Linear algebra and its applicationsinJournal
2022The geometry of discotopes
In: Le MatematicheinJournal
2022A note on overrelaxation in the Sinkhorn algorithm
In: Optimization lettersinJournal
2022A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions
In: Journal of optimization theory and applicationsinJournal
2021Existence of dynamical low-rank approximations to parabolic problems
In: Mathematics of computationinJournal
2021Jordan algebras of symmetric matrices
In: Le MatematicheinJournal
2021The degree of Stiefel manifolds
In: Enumerative combinatorics and applicationsinJournal
2021