My research is on large-scale and high-dimensional problems that are solved numerically using low-rank matrix and tensor techniques. Examples of such problems are the electronic Schrödinger equation, parametric partial differential equations, and low-rank matrix completion. I tend to focus on practical algorithms that can be formulated on Riemannian matrix manifolds and use techniques from numerical linear algebra and numerical optimization. My other research interests include nonlinear eigenvalue problems, machine learning, and multilevel preconditioning.
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| [23] | Automatic rational approximation and linearization of nonlinear eigenvalue problems
P. Lietaert, K. Meerbergen, J. Pérez, B. Vandereycken
In IMA Journal of Numerical Analysis, 2021.
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| [22] | Riemannian multigrid line search for low-rank problems
M. Sutti, B. Vandereycken
In SIAM J. Sci. Comput., 2021.
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| [21] | On critical points of quadratic low-rank matrix optimization problems
A. Uschmajew, B. Vandereycken
In IMA J. Numer. Anal., 2020.
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| [20] | Explicit stabilised gradient descent for faster strongly convex optimisation
A. Eftekhari, B. Vandereycken, G. Vilmart, K. Zygalakis
In BIT Numer. Math., 2020.
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| [19] | A globally convergent method to compute the real stability radius for time-delay systems
F. Borgioli, W. Michiels, D. Lu, B. Vandereycken
In Systems & Control Letters, volume 127, 2019.
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| [18] | Time integration of rank-constrained Tucker tensors
Ch. Lubich, H. Walach, B. Vandereycken
In SIAM J. Numer. Anal., volume 56, 2018.
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| [17] | Subspace acceleration for the Crawford number and related eigenvalue optimization problems
D. Kressner, D. Lu, B. Vandereycken
In SIAM J. Matrix Anal. Appl., volume 39, 2018.
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| [16] | Projection Methods for Dynamical Low-Rank Approximation of High-Dimensional Problems
E. Kieri, B. Vandereycken
In Comput. Meth. Appl. Math., volume 19, 2018.
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| [15] | Robust Rayleigh quotient minimization and nonlinear eigenvalue problems
Z. Bai, D. Lu, B. Vandereycken
In SIAM J. Sci. Comput., volume 40, 2018.
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| [14] | Criss-cross type algorithms for computing the real pseudospectral abscissa
D. Lu, B. Vandereycken
In SIAM J. Matrix Anal. Appl., volume 38, 2017.
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| [13] | Circadian lipidomics reveals diurnal lipid oscillations in human skeletal muscle persisting in cellular myotubes cultured in vitro
U. Loizides-Mangold, L. Perrin, B. Vandereycken, J. A. Betts, J.-P. Walhin, I. Templeman, S. Chanon, B. D. Weger, C. Durand, M. Robert, J. Paz, M. Moniatte, L. G. Karagounis, J. D. Johnston, F. Gachon, E. Lefai, H. Riezman, C. Dibner
In Proc. Natl. Acad. Sci. USA, volume 114, 2017.
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| [12] | Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure
D. Kressner, M. Steinlechner, B. Vandereycken
In SIAM J. Sci. Comput., volume 38, 2016.
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| [11] | Unifying time evolution and optimization with matrix product states
J. Haegeman, Ch. Lubich, I. Oseledets, B. Vandereycken, F. Verstraete
In Phys. Rev. B, volume 94, 2016.
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| [10] | Time integration of tensor trains
Ch. Lubich, I. Oseledets, B. Vandereycken
In SIAM J. Numer. Anal., volume 53, 2015.
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| [9] | Subspace methods for computing the pseudospectral abscissa and the stability radius
D. Kressner, B. Vandereycken
In SIAM J. Matrix Anal. Appl., volume 35, 2014.
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| [8] | Low-Rank tensor completion by Riemannian optimization
D. Kressner, M. Steinlechner, B. Vandereycken
In BIT Numer. Math., volume 54, 2014.
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| [7] | Low-rank matrix completion by Riemannian optimization
B. Vandereycken
In SIAM J. Optim., volume 23, 2013.
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| [6] | The geometry of algorithms using hierarchical tensors
A. Uschmajew, B. Vandereycken
In Lin. Alg. Appl., volume 439, 2013.
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| [5] | Dynamical approximation of hierarchical Tucker and tensor-train tensors
Ch. Lubich, T. Rohwedder, R. Schneider, B. Vandereycken
In SIAM J. Matrix Anal. Appl., volume 34, 2013.
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| [4] | A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank
B. Vandereycken, P.-A. Absil, S. Vandewalle
In IMA J. Numer. Anal., volume 33, 2012.
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| [3] | A survey and comparison of contemporary algorithms for computing the matrix geometric mean
B. Jeuris, R. Vandebril, B. Vandereycken
In ETNA, volume 39, 2012.
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| [2] | A Riemannian optimization approach for computing low-rank solutions of Lyapunov equations
B. Vandereycken, S. Vandewalle
In SIAM J. Matrix Anal. Appl., volume 31, 2010.
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| [1] | The smoothed spectral abscissa for robust stability optimization
J. Vanbiervliet, B. Vandereycken, W. Michiels, S. Vandewalle, M. Diehl
In SIAM J. Optim., volume 20, 2009.
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