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 and numerical optimization. My other research interests include nonlinear eigenvalue problems, machine learning, and multilevel preconditioning.

Publications

Submitted

2018
[3]On critical points of quadratic low-rank matrix optimization problems
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Tech. report (submitted), .
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[2]Automatic rational approximation and linearization of nonlinear eigenvalue problems
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Tech. report (submitted), .
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[1]Robust Rayleigh quotient minimization and nonlinear eigenvalue problems
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Tech. report (submitted), .
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Published journal articles

2018
[17]Time integration of rank-constrained Tucker tensors
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In SIAM J. Numer. Anal., volume 56, .
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[16]Subspace acceleration for the Crawford number and related eigenvalue optimization problems
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In SIAM J. Matrix Anal. Appl., volume 39, .
[more]
[15]Projection methods for dynamical low-rank approximation of high-dimensional problems
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In CMAM (to appear), .
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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]Circadian lipidomics reveals diurnal lipid oscillations in human skeletal muscle persisting in cellular myotubes cultured in vitro
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In Proc. Natl. Acad. Sci. USA, volume 114, .
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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
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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
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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
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In ICML 2014, volume 32, .
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2009
[1]Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank
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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.

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