Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 53, Issue 2, Pages 917-941Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140976546
Keywords
tensor train; matrix product state; low-rank approximation; time-varying tensors; tensor differential equations; splitting integrator
Categories
Funding
- DFG [SPP 1324, GRK 1838]
- Russian Science Foundation [14-11-00659]
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A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train/matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formulation, implementation, and theoretical properties of the proposed integrator are studied, and numerical experiments with problems from quantum molecular dynamics and with iterative processes in the tensor train format are included.
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