DMRG approach to fast linear algebra in the TT-format

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)

Abstract

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 http://spring.inm.ras.ru/osel.

Original languageEnglish
Pages (from-to)382-393
Number of pages12
JournalComputational Methods in Applied Mathematics
Volume11
Issue number3
DOIs
Publication statusPublished - 2011
Externally publishedYes

Keywords

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

Fingerprint

Dive into the research topics of 'DMRG approach to fast linear algebra in the TT-format'. Together they form a unique fingerprint.

Cite this