Zobrazeno 1 - 10
of 34
pro vyhledávání: '"André Uschmajew"'
Publikováno v:
Frontiers in Applied Mathematics and Statistics, Vol 8 (2022)
Externí odkaz:
https://doaj.org/article/db8d7c243c4e401ab3528e5db4a0cf25
Publikováno v:
SIAM Journal on Scientific Computing. 43:A586-A608
In this work, the task to find a simultaneous low rank approximation of several lowest eigenpairs of a matrix-valued symmetric operator is considered. This problem arises, for instance, in the dens...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ac9995296e78bda2833b86fb9696ca5
https://doi.org/10.1137/19m1308384
https://doi.org/10.1137/19m1308384
Autor:
André Uschmajew, Bart Vandereycken
Based on a result by Taylor, Hendrickx, and Glineur (J. Optim. Theory Appl., 178(2):455--476, 2018) on the attainable convergence rate of gradient descent for smooth and strongly convex functions in terms of function values, an elementary convergence
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ed7bed631c77bd867402fcd88c02bc2
https://opus.bibliothek.uni-augsburg.de/opus4/files/103113/s10957-022-02032-z.pdf
https://opus.bibliothek.uni-augsburg.de/opus4/files/103113/s10957-022-02032-z.pdf
Publikováno v:
Frontiers Research Topics ISBN: 9782832504253
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::be9e1838afc41109f1c2de17807433cf
https://doi.org/10.3389/978-2-8325-0425-3
https://doi.org/10.3389/978-2-8325-0425-3
A Gradient Sampling Method on Algebraic Varieties and Application to Nonsmooth Low-Rank Optimization
Publikováno v:
SIAM Journal on Optimization. 29:2853-2880
In this paper, a nonsmooth optimization method for locally Lipschitz functions on real algebraic varieties is developed. To this end, the set-valued map $\varepsilon$-conditional subdifferential $x...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d64a4adea6014f49a29ec2778cbe583a
https://doi.org/10.1137/17m1153571
https://doi.org/10.1137/17m1153571
In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular, a Riemannian version of IHT is considered which significantly reduces computational cost
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c73f8487e1cf9462b231d8e41f5419aa
Autor:
Wolfgang Hackbusch, André Uschmajew
A modification of standard linear iterative methods for the solution of linear equations is investigated aiming at improved data-sparsity with respect to a rank function. The convergence speed of the modified method is compared to the rank growth of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14154010659802a6d6362a222540f234
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103115
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103115
Autor:
Henrik Eisenmann, André Uschmajew
It is shown that the relative distance in Frobenius norm of a real symmetric order-$d$ tensor of rank two to its best rank-one approximation is upper bounded by $\sqrt{1-(1-1/d)^{d-1}}$. This is achieved by determining the minimal possible ratio betw
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89a489265e22e2dada738fa591cc7e55
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f605aeb142d08da7e34842af516b54f
http://arxiv.org/abs/2002.12197
http://arxiv.org/abs/2002.12197
Autor:
Bart Vandereycken, André Uschmajew
Publikováno v:
Handbook of Variational Methods for Nonlinear Geometric Data ISBN: 9783030313500
Scopus-Elsevier
Scopus-Elsevier
In this chapter we present numerical methods for low-rank matrix and tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus on two types of problems: The first are optimization problems, like m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::554b6733cb82e3de0439fe608efc1f05
https://doi.org/10.1007/978-3-030-31351-7_9
https://doi.org/10.1007/978-3-030-31351-7_9