DMRG approach to fast linear algebra in the TT-format

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37 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)382-393
Number of pages12
JournalComputational Methods in Applied Mathematics
Issue number3
Publication statusPublished - 2011
Externally publishedYes


  • High-dimensional problem
  • SVD
  • Tensors
  • TT-format


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