## Preliminary list of abstracts

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- Dolgov, Sergey (Institute of Numerical Mathematics, Russian Academy of Sciences, Russia)

The Matrix Product State representation and the Density Matrix Renormalization Group algorithms are widely used in the quantum physics community to describe and compute quantum states of one-dimensional spin chains. Independently the so-called TT and QTT formats were discovered by E. Tyrtyshnikov and I. Oseledets as tensor approximation techniques. Nevertheless, these formats exploit the similar MPS like structure. Thus the idea of an application of the DMRG approach to quite general high-dimensional problems in the QTT format arose. In this work we consider a solution to a parabolic equation with implicit time-propagating schemes. The main point is the usage of the DMRG approach only for the approximate Matrix-by-Vector operation and the solution of a linear system without using special time-dependent DMRG methods. We present and compare two approaches: the solution of the linear system arising in the implicit scheme at each time step, and precomputation of the inverse matrix in order to apply only MatVec at the time step.