Page 446 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 446
MATRIX COMPUTATIONS AND NUMERICAL (MS-47)
in at most two additive terms in the equation has been extensively studied, and satisfactory so-
lution strategies have been developed for various classes of problems, both in the small and
large scale cases. The general multiterm setting is regarded as far more complicated, and only
recently practical solution methods have been proposed. In this talk we discuss new procedures
that can take advantage of certain algebraic properties of the coefficient matrices, yielding ef-
fective algorithms both in terms of computational time and memory requirements.
Part of this work is joint with Yue Hao, School of Mathematics and Statistics, Lanzhou
University, (PRC).
Riemannian thresholding methods for row-sparse and low-rank matrix
recovery
André Uschmajew, uschmajew@mis.mpg.de
MPI MiS Leipzig, Germany
The problem of recovering a jointly row-sparse and low-rank matrix from linear measurements
arises for instance in sparse blind deconvolution. The ideal goal is to ensure recovery using
only a minimal number of measurements with respect to the combined constraints. We present
modifications of the iterative hard thresholding (IHT) method for this task. In particular a
Riemannian version of IHT is considered which significantly reduces computational cost of
the gradient projection in the case of rank-one measurements. We also consider a Riemannian
proximal gradient method for the special case of unknown sparsity. This is joint work with H.
Eisenmann, F. Krahmer and M. Pfeffer.
444
in at most two additive terms in the equation has been extensively studied, and satisfactory so-
lution strategies have been developed for various classes of problems, both in the small and
large scale cases. The general multiterm setting is regarded as far more complicated, and only
recently practical solution methods have been proposed. In this talk we discuss new procedures
that can take advantage of certain algebraic properties of the coefficient matrices, yielding ef-
fective algorithms both in terms of computational time and memory requirements.
Part of this work is joint with Yue Hao, School of Mathematics and Statistics, Lanzhou
University, (PRC).
Riemannian thresholding methods for row-sparse and low-rank matrix
recovery
André Uschmajew, uschmajew@mis.mpg.de
MPI MiS Leipzig, Germany
The problem of recovering a jointly row-sparse and low-rank matrix from linear measurements
arises for instance in sparse blind deconvolution. The ideal goal is to ensure recovery using
only a minimal number of measurements with respect to the combined constraints. We present
modifications of the iterative hard thresholding (IHT) method for this task. In particular a
Riemannian version of IHT is considered which significantly reduces computational cost of
the gradient projection in the case of rank-one measurements. We also consider a Riemannian
proximal gradient method for the special case of unknown sparsity. This is joint work with H.
Eisenmann, F. Krahmer and M. Pfeffer.
444
