· 2016· Preprint
Time integration of tensor trains
- 172citations
- 2016year
Short summary
A new time integrator for dynamical tensor approximation in the tensor train/matrix product state format is presented, based on splitting the projector onto the tangent space of the tensor manifold.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces a novel time integrator for tensor train/matrix product state formats.
- The method relies on splitting the projector onto the tangent space of the tensor manifold.
- Enables updating time-dependent tensors and solving tensor differential equations.
- Tested on quantum molecular dynamics and iterative tensor train processes.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. 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. Key words. Tensor train, matrix product state, low-rank approximation, time-varying tensors, tensor differential equations, splitting integrator. AMS subject classifications. 15A18,15A69,65F99,65L05 1. Introduction. In
The authors' abstract, as published at the source., 2016 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Computational Mathematics
Computational MathematicsMathematics