6 papers
A counterexample to the symmetric-maximizer conjecture for Lyapunov operators
Daniel Kressner, Bart Vandereycken
It has been conjectured that the operator norm of the Lyapunov operator induced by the Frobenius norm is always attained at a symmetric matrix. The conjecture is known to hold for…
Interpolatory Dynamical Low-Rank Approximation: Theoretical Foundations and Algorithms
Benjamin Carrel, Daniel Kressner, Hei Yin Lam +1
Dynamical low-rank approximation (DLRA) is a widely used paradigm for solving large-scale matrix differential equations, as they arise, for example, from the discretization of time…
Gauss-Southwell type descent methods for low-rank matrix optimization
Guillaume Olikier, André Uschmajew, Bart Vandereycken
We consider gradient-related methods for low-rank matrix optimization with a smooth cost function. The methods operate on single factors of the low-rank factorization and share asp…
Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints: an extended version
Shixin Zheng, Wen Huang, Bart Vandereycken +1
For smooth optimization problems with a Hermitian positive semi-definite fixed-rank constraint, we consider three existing approaches including the simple Burer--Monteiro method, a…
A geodesic convexity-like structure for the polar decomposition of a square matrix
Foivos Alimisis, Bart Vandereycken
We make a full landscape analysis of the (generally non-convex) orthogonal Procrustes problem. This problem is equivalent to computing the polar factor of a square matrix. We revea…
A preconditioned inverse iteration with an improved convergence guarantee
Foivos Alimisis, Daniel Kressner, Nian Shao +1
Preconditioned eigenvalue solvers offer the possibility to incorporate preconditioners for the solution of large-scale eigenvalue problems, as they arise from the discretization of…