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.
|||A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions|
Tech. report (submitted), 2021.
|||The leapfrog algorithm as nonlinear Gauss–Seidel|
Tech. report (submitted), 2020.
|||Geometric methods on low-rank matrix and tensor manifolds|
Chapter in Variational methods for nonlinear geometric data and applications (P. Grohs, M. Holler, A. Weinmann, eds.), Springer, 2020.
Published journal articles
Refereed conference papers
|||Riemannian and multilevel optimization for rank-constrained matrix problems|
PhD thesis, Department of Computer Science, KU Leuven, 2010.
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.