From low-rank retractions to dynamical low-rank approximation and back

• Published in: BIT Vol. 64; no. 3; p. 25
• Main Authors: Séguin, Axel, Ceruti, Gianluca, Kressner, Daniel
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2024; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computational Mathematics and Numerical Analysis; Differential equations; Integrators; Manifolds; Mathematics; Mathematics and Statistics; Numeric Computing; Numerical integration; Research Paper; Truncation errors; Dynamical low-rank approximation; 65L05; 65L20; Retraction; Time integration

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for other computational tasks on manifold as well,...