4 papers · 1 filter
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…
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…