An unconventional robust integrator for dynamical low-rank approximation
| Autor: | Gianluca Ceruti, Christian Lubich |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Multilinear map
Matrix differential equation Rank (linear algebra) Computer Networks and Communications Differential equation Applied Mathematics Low-rank approximation Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Matrix (mathematics) Integrator FOS: Mathematics Applied mathematics Tensor Mathematics - Numerical Analysis 0101 mathematics Software Mathematics |
| Popis: | We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation. Furthermore, the integrator is extended to the approximation of time-dependent tensors by Tucker tensors of fixed multilinear rank. The proposed low-rank integrator is different from the known projector-splitting integrator for dynamical low-rank approximation, but it retains the important robustness to small singular values that has so far been known only for the projector-splitting integrator. The new integrator also offers some potential advantages over the projector-splitting integrator: It avoids the backward time integration substep of the projector-splitting integrator, which is a potentially unstable substep for dissipative problems. It offers more parallelism, and it preserves symmetry or anti-symmetry of the matrix or tensor when the differential equation does. Numerical experiments illustrate the behaviour of the proposed integrator. arXiv admin note: text overlap with arXiv:1906.01369 |
| Databáze: | OpenAIRE |
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