publication . Other literature type . Article . Preprint . 2014

Time Integration of Tensor Trains

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart;
  • Published: 08 Jul 2014
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
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 ite...
Subjects
ACM Computing Classification System: MathematicsofComputing_NUMERICALANALYSISComputingMethodologies_COMPUTERGRAPHICSComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
free text keywords: Symmetric tensor, Tensor product of Hilbert spaces, Tensor, Mathematical optimization, Mathematical analysis, Tensor field, Mathematics, Tensor density, Tensor contraction, Tensor (intrinsic definition), Cartesian tensor, Mathematics - Numerical Analysis, 15A18, 15A69, 65F99, 65L05
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