Bart Vandereycken

Bart Vandereycken Postdoctoral researcher Chair of Numerical Algorithms and High-Performance Computing Mathematics Institute of Computational Science and Engineering École Polytechnique Fédérale de Lausanne, EPFL

Contact

EPFL SB-Mathicse-ANCHP
MA B2 525
Station 8
CH-1015 Lausanne
Switzerland

Phone: + 41 21 69 32 553
Fax: + 41 21 69 34 304
Email:

Interests and current research

• High-dimensional PDEs: low-rank matrix and tensor techniques, multilevel preconditioning, model-order reduction.

• Computational differential geometry: optimization on manifolds, matrix means, geometry of matrix and tensor spaces, manifold learning.

• Numerical linear algebra: pseudospectra, low-rank tensors, numerics of PDEs.

Full papers (journal articles and technical reports)

1. A survey and comparison of contemporary algorithms for computing the matrix geometric mean (with B. Jeuris and R. Vandebril)
   Submitted (2012)  —  pdf, code, bibtex

   @techreport{JeurVV:2012,
     Author = {B. Jeuris and R. Vandebril and B. Vandereycken},
     Institution = {ANCHP-MATHICSE, Mathematics Section, {'E}cole Polytechnique F{'e}d{'e}rale de Lausanne},
     Title = {A survey and comparison of contemporary algorithms for computing the matrix geometric mean},
     Year = {2012}
   }
   

2. Subspace methods for computing the pseudospectral abscissa and the stability radius (with D. Kressner)
   Submitted (2012)  —  pdf, code, bibtex

   @techreport{KressV:2012,
     Author = {D. Kressner and B. Vandereycken},
     Institution = {ANCHP-MATHICSE, Mathematics Section, {'E}cole Polytechnique F{'e}d{'e}rale de Lausanne},
     Title = {Subspace methods for computing the pseudospectral abscissa and the stability radius},
     Year = {2012}
   }
   

3. The geometry of algorithms using hierarchical tensors (with A. Uschmajew)
   Submitted (2012)  —  pdf, code, bibtex

   @techreport{UschmV:2012,
     Author = {A. Uschmajew and B. Vandereycken},
     Institution = {ANCHP-MATHICSE, Mathematics Section, {'E}cole Polytechnique F{'e}d{'e}rale de Lausanne},
     Title = {The geometry of algorithms using hierarchical tensors},
     Year = {2012}
   }
   

4. Low-rank matrix completion by Riemannian optimization
   Submitted (2011)  —  pdf, code, bibtex

   @techreport{Vand:2011,
     Author = {B. Vandereycken},
     Institution = {ANCHP-MATHICSE, Mathematics Section, {'E}cole Polytechnique F{'e}d{'e}rale de Lausanne},
     Title = {Low-rank matrix completion by Riemannian optimization},
     Year = {2011}
   }
   

5. A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank (with P.-A. Absil and S. Vandewalle)
   to appear in IMA J. Numer. Anal. (2012)  —  pdf, bibtex

   @article{VandAV:2012,
     Author = {B. Vandereycken and {P.-A.} Absil and S. Vandewalle},
     Journal = {IMA Journal of Numerical Analysis},
     Title = {A {R}iemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank},
     Year = {2012},
     Note = {To appear}
   }
   

6. A Riemannian optimization approach for computing low-rank solutions of Lyapunov equations (with S. Vandewalle)
   SIAM J. Matrix Anal. Appl. 31:5 (2010): 2553-2579  —  pdf, doi, bibtex

   @article{VandV:2010,
     Author = {B. Vandereycken and S. Vandewalle},
     Journal = {SIAM Journal on Matrix Analysis and Applications},
     Number = {5},
     Pages = {2553--2579},
     Title = {A {R}iemannian optimization approach for computing low-rank solutions of {L}yapunov equations},
     Volume = {31},
     Year = {2010}
   }
   

Awarded the 15th Leslie Fox Prize in Numerical Analysis (second place)

7. The smoothed spectral abscissa for robust stability optimization (with J. Vanbiervliet, W. Michiels, S. Vandewalle, and M. Diehl)
   SIAM J. Optim. 20:1 (2009): 156-171  —  pdf, doi, bibtex

   @article{VanbVMVD:2009,
     Author = {J. Vanbiervliet and B. Vandereycken and W. Michiels and S. Vandewalle and M. Diehl},
     Journal = {SIAM Journal on Optimization},
     Number = {1},
     Pages = {156--171},
     Title = {The smoothed spectral abscissa for robust stability optimization},
     Volume = {20},
     Year = {2009}
   }
   

Selected refereed conference papers

1. Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank (with P.-A. Absil and S. Vandewalle)
   Proc. of the IEEE 15th SSP (2009): 389-392  —  doi, pdf, bibtex

   @inproceedings{VandAV:2009,
     Author = {B. Vandereycken and P.-A. Absil and S. Vandewalle},
     Booktitle = {Proceedings of the IEEE 15th Workshop on Statistical Signal Processing},
     Pages = {389--392},
     Title = {Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank},
     Year = {2009}
   }
   

Other publications

1. Riemannian and multilevel optimization for rank-constrained matrix problems
   PhD thesis (December 2010)  —  pdf, bibtex

   @phdthesis{PhDVandereycken:2010,
     Author = {B. Vandereycken},
     School = {Department of Computer Science, Katholieke Universiteit Leuven},
     Title = {Riemannian and multilevel optimization for rank-constrained matrix problems},
     Year = {2010}
   }
   

Awarded the Alston S. Householder Award XIV

Software

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

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

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