Bart Vandereycken

Research interests

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. My other research interests include pseudospectra, matrix means, model-order reduction, and multilevel preconditioning.

Publications

Submitted

2017
[4]Time integration of rank-constrained Tucker tensors
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Tech. report (submitted), .
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[3]Subspace acceleration for the Crawford number and related eigenvalue optimization problems
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Tech. report (submitted), .
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[2]Projection methods for dynamical low-rank approximation of high-dimensional problems
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Tech. report (submitted), .
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[1]Robust Rayleigh quotient minimization and nonlinear eigenvalue problems
, ,
Tech. report (submitted), .
[more]

Published journal articles

2017
[14]Criss-cross type algorithms for computing the real pseudospectral abscissa
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In SIAM J. Matrix Anal. Appl., volume 38, .
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[13]Lipidomics reveals diurnal lipid oscillations in human skeletal muscle persisting in cellular myotubes cultured in vitro
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In PNAS (Early access), .
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2016
[12]Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure
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In SIAM J. Sci. Comput., volume 38, .
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[11]Unifying time evolution and optimization with matrix product states
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In Phys. Rev. B, volume 94, .
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2015
[10]Time integration of tensor trains
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In SIAM J. Numer. Anal., volume 53, .
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2014
[9]Subspace methods for computing the pseudospectral abscissa and the stability radius
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In SIAM J. Matrix Anal. Appl., volume 35, .
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[8]Low-Rank tensor completion by Riemannian optimization
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In BIT Numer. Math., volume 54, .
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2013
[7]Low-rank matrix completion by Riemannian optimization

In SIAM J. Optim., volume 23, .
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[6]The geometry of algorithms using hierarchical tensors
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In Lin. Alg. Appl., volume 439, .
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[5]Dynamical approximation of hierarchical Tucker and tensor-train tensors
, , ,
In SIAM J. Matrix Anal. Appl., volume 34, .
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2012
[4]A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank
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In IMA J. Numer. Anal., volume 33, .
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[3]A survey and comparison of contemporary algorithms for computing the matrix geometric mean
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In ETNA, volume 39, .
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2010
[2]A Riemannian optimization approach for computing low-rank solutions of Lyapunov equations
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In SIAM J. Matrix Anal. Appl., volume 31, .
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2009
[1]The smoothed spectral abscissa for robust stability optimization
, , , ,
In SIAM J. Optim., volume 20, .
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Refereed conference papers

2015
[3]Greedy rank updates combined with Riemannian descent methods for low-rank optimization
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In Sampling Theory and Applications (SampTA), 2015 International Conference on, IEEE, .
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2014
[2]Riemannian pursuit for big matrix recovery
, , , ,
In ICML 2014, volume 32, .
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2009
[1]Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank
, ,
In SSP09, .
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Ph.D thesis

2010
[1]Riemannian and multilevel optimization for rank-constrained matrix problems

PhD thesis, Department of Computer Science, KU Leuven, .
[more]

Software

  1. MATLAB code for the paper Robust Rayleigh quotient minimization and nonlinear eigenvalue problems: see here.

  2. MATLAB code for the paper Subspace acceleration for the Crawford number and related eigenvalue optimization problems: see here.

  3. MATLAB code for the paper Criss-cross type algorithms for computing the real pseudospectral abscissa: see here.

  4. Python code for the paper Time integration of tensor trains: email me, code cannot be distributed because of copyright of 3rd party code.

  5. MATLAB code for the paper A Riemannian approach to low-rank algebraic Riccati equations: see here.

  6. MATLAB code for the paper Subspace methods for computing the pseudospectral abscissa and the stability radius: see here.

  7. MATLAB code for the paper The geometry of algorithms using hierarchical tensors: see here.

  8. MATLAB code for the paper Low-rank matrix completion by Riemannian optimization: see here.

  9. MATLAB code for the paper Low-rank tensor completion by Riemannian optimization: see here.