publication . Other literature type . Preprint . Article . 2014

Time Integration of Tensor Trains

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