7 citations · 19 across the 13 of their papers we have counts for
14 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…
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…
A Nesterov-style Accelerated Gradient Descent Algorithm for the Symmetric Eigenvalue Problem
Foivos Alimisis, Simon Vary, Bart Vandereycken
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-defi…
Projected exponential methods for stiff dynamical low-rank approximation problems
Benjamin Carrel, Bart Vandereycken
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of…
Gradient-type subspace iteration methods for the symmetric eigenvalue problem
Foivos Alimisis, Yousef Saad, Bart Vandereycken
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new varian…
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…
Implicit low-rank Riemannian schemes for the time integration of stiff partial differential equations
Marco Sutti, Bart Vandereycken
We propose two implicit numerical schemes for the low-rank time integration of stiff nonlinear partial differential equations. Our approach uses the preconditioned Riemannian trust…
Randomized sketching of nonlinear eigenvalue problems
Stefan Güttel, Daniel Kressner, Bart Vandereycken
Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anders…
Geodesic Convexity of the Symmetric Eigenvalue Problem and Convergence of Riemannian Steepest Descent
Foivos Alimisis, Bart Vandereycken
We study the convergence of the Riemannian steepest descent algorithm on the Grassmann manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix. Eve…
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…
Low-rank Parareal: a low-rank parallel-in-time integrator
Benjamin Carrel, Martin J. Gander, Bart Vandereycken
In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used…
Riemannian multigrid line search for low-rank problems
Marco Sutti, Bart Vandereycken
Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this p…