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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.