DMRG Approach to Fast Linear Algebra in the TT-Format

Ivan Oseledets 1
  • 1 Institute of Numerical Mathematics, Russian Academy of Sciences, 8 Gubkin Street, Moscow, Russia.


In this paper, the concept of the DMRG minimization scheme is extended to several important operations in the TT-format, like the matrix-by-vector product and the conversion from the canonical format to the TT-format. Fast algorithms are implemented and a stabilization scheme based on randomization is proposed. The comparison with the direct method is performed on a sequence of matrices and vectors coming as approximate solutions of linear systems in the TT-format. A generated example is provided to show that randomization is really needed in some cases. The matrices and vectors used are available from the author or at

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