## 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 SchrĂ¶dinger 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

### Book chapters

### Published journal articles

### Refereed conference papers

### Ph.D thesis

2010 | |

[1] | Riemannian and multilevel optimization for rank-constrained matrix problems PhD thesis, Department of Computer Science, KU Leuven, 2010. |

## Software

MATLAB code for the paper

*RMGLS: A MATLAB algorithm for Riemannian multilevel optimization*: see here.MATLAB code for the paper

*Automatic rational approximation and linearization of nonlinear eigenvalue problems*: download autoCORK.MATLAB code for the paper

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

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

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

*Time integration of tensor trains*: email me, code cannot be distributed because of copyright of 3rd party code.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.