• I am a co-developer of TT-Toolbox: an open-source object-oriented MATLAB/C/Fortran package for computations in the Tensor Train and QTT-Tucker tensor product formats.
    Main features include:
    • Overloaded linear algebra with matrices and vectors in a tensor format.
    • Compression of given data into a format by direct (SVD) and sparse (cross) procedures.
    • A collection of examples with analytical tensor formats (finite difference Laplacian, etc.)
    • Alternating iterative algorithms for solution of linear systems and eigenvalue problems.
  • tAMEn: purely Matlab routines for alternating iterative solution of the ordinary differential equations in the tensor train format.
    See “A tensor decomposition algorithm for large ODEs with conservation laws”, [arXiv:1403.8085].
    The main feature of the new algorithm is the spectral accuracy in time and the possibility to conserve linear invariants and the second norm up to the machine (not tensor approximation) precision.
    Another difference with TT-Toolbox is the storage scheme, which allows sparse tensor product factors.

    New: adaptive time discretisation.

  • ALS-Cross algorithm: First try of a Tensor Train Uncertainty Quantification toolkit.
    A combination of the ALS and TT Cross algorithms, together with high-level drivers for solving stochastic and parametric PDEs (a.k.a. high-dimensional linear systems with block-diagonal matrices).