Bart Vandereycken |

Department of Mathematics

Princeton University

Fine Hall, Washington Road

Princeton NJ 08544-1000

Fax: +1 609 258 1735

Office: 1009

Email:

Numerical analysis, in particular:

*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.

Fall 2014: MAT321 Numerical Methods

Spring 2014: MAT321 Numerical Methods

Fall 2013: MAT203 Advanced Vector Calculus

Spring 2013: MAT202 Introduction to Linear Algebra

Fall 2012: MAT321 Numerical Methods

**Unifying time evolution and optimization with matrix product states**

with J. Haegeman, C. Lubich, I. Oseledets, and F. Verstraete**Time integration of tensor trains**

with C. Lubich and I. Oseledets

**Subspace methods for computing the pseudospectral abscissa and the stability radius**

with D. Kressner**Low-rank tensor completion by Riemannian optimization**

with D. Kressner and M. Steinlechner**The geometry of algorithms using hierarchical tensors**

with A. Uschmajew**Dynamical approximation by hierarchical Tucker and tensor-train tensors**

with C. Lubich, T. Rohwedder, and R. Schneider**A survey and comparison of contemporary algorithms for computing the matrix geometric mean**

with B. Jeuris and R. Vandebril**A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank**

with P.-A. Absil and S. Vandewalle**A Riemannian optimization approach for computing low-rank solutions of Lyapunov equations**

with S. Vandewalle

→ Awarded the 15th Leslie Fox Prize in Numerical Analysis (second place) and the SIAM Outstanding Paper Prize.**The smoothed spectral abscissa for robust stability optimization**

with J. Vanbiervliet, W. Michiels, S. Vandewalle, and M. Diehl

**Line-search methods and rank increase on low-rank matrix varieties**

with A. Uschmajew**A Riemannian approach to low-rank algebraic Riccati equations**

with B. Mishra**Riemannian pursuit for big matrix recovery**

with M. Tan, I. Tsang, L. Wang, and S. Pan**Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank**

with P.-A. Absil and S. Vandewalle

**Riemannian and multilevel optimization for rank-constrained matrix problems**

PhD thesis (December 2010)

→ Awarded the Alston S. Householder Award XIV

Python code for the paper

*Time integration of tensor trains*: soon available.MATLAB code for the paper

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

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

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

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

*Low-rank tensor completion by Riemannian optimization*: see here.