An unconventional robust integrator for dynamical low-rank approximation

2020/10/02 by Ceruti, Gianluca, Lubich, Christian · 15 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2010.02022

Abstract

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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Related

• Time integration of symmetric and anti-symmetric low-rank matrices and\n Tucker tensors
• Time integration of rank-constrained Tucker tensors
• A projector-splitting integrator for dynamical low-rank approximation
• A rank-adaptive robust integrator for dynamical low-rank approximation
• Second-order robust parallel integrators for dynamical low-rank approximation