Time integration of rank-constrained Tucker tensors
| Autor: | Hanna Walach, Christian Lubich, Bart Vandereycken |
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| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Rank (linear algebra) Differential equation Applied Mathematics MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics Numerical Analysis (math.NA) 01 natural sciences 010101 applied mathematics Computational Mathematics Singular value Matrix (mathematics) Discrete time and continuous time Integrator ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Optimization methods FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis Tensor 0101 mathematics Mathematics ComputingMethodologies_COMPUTERGRAPHICS |
| DOI: | 10.48550/arxiv.1709.02594 |
| Popis: | Dynamical low-rank approximation in the Tucker tensor format of given large time-dependent tensors and of tensor differential equations is the subject of this paper. In particular, a discrete time integration method for rank-constrained Tucker tensors is presented and analyzed. It extends the known projector-splitting integrator for dynamical low-rank approximation of matrices to Tucker tensors and is shown to inherit the same favorable properties. The integrator is based on iteratively applying the matrix projector-splitting integrator to tensor unfoldings but with inexact solution in a substep. It has the property that it reconstructs time-dependent Tucker tensors of the given rank exactly. The integrator is also shown to be robust to the presence of small singular values in the tensor unfoldings. Numerical examples with time-dependent problems from quantum physics and tensor optimization methods illustrate our theoretical results. |
| Databáze: | OpenAIRE |
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