A rank-adaptive robust integrator for dynamical low-rank approximation

• Published in: BIT Vol. 62; no. 4; pp. 1149 - 1174
• Main Authors: Ceruti, Gianluca, Kusch, Jonas, Lubich, Christian
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2022; Springer Nature B.V
• Subjects: Approximation; Computational Mathematics and Numerical Analysis; Differential equations; Gradient flow; Hamiltonian functions; Integrators; Mathematical analysis; Mathematics; Mathematics and Statistics; Numeric Computing; Robustness (mathematics); Schrodinger equation; Subspaces; Tensors; Dynamical low-rank approximation; 65L05; Rank adaptivity; 65L70; 65L20; 15A69; Structure-preserving integrator; Matrix and tensor differential equations

A rank-adaptive integrator for the dynamical low-rank approximation of matrix and tensor differential equations is presented. The fixed-rank integrator recently proposed by two of the authors is extended to allow for an adaptive choice of the rank, using subspaces that are generated by the integrato...