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An unconventional robust integrator for dynamical low-rank approximation

Ceruti, Gianluca; Lubich, Christian

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.

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Volltext §
DOI: 10.5445/IR/1000131728
Veröffentlicht am 22.04.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 12.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000131728
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 19 S.
Serie CRC 1173 Preprint ; 2020/41
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter dynamical low-rank approximation, structure-preserving integrator, matrix and tensor differential equations, Tucker tensor format
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