Working with tensor-structured matrices and vectors

01/07/2008

A new publication on tensor-structured matrices, with a tentative title “Linear algebra for tensor problems” is added. It is submitted to the special issue of Computing.

This paper is about  structured iterations with matrices of low tensor rank in three dimensions. We show that in three dimensions we can use Tucker decomposition instead of the canonical decomposition without any substantial increase in the computational cost. To achieve this goal we have to compute quite complex six-fold sum, but it is shown that they can be computed with calls to BLAS/LAPACK. Therefore Tucker format is highly recommended for 3-dimensional problems. With a current MATLAB code (will be posted here soon)  it is possible to handle dense matrices (i.e., approximate inversion) on a grid of size 256^3.  In a future research by using additional approximation techniques we will be able to increase this number to at least 1024^3.

News

26/05/2016 A TT-eigenvalue solver that finally works
12/05/2016 Exponential machines and tensor trains
06/04/2016 Convergence analysis of a projected fixed-point iteration
30/03/2016 Compress-and-eliminate solver for sparse matrices
01/12/2015 New paper in SIMAX

Contact

We are located at the 2-nd floor of the new "Technopark-3” building in Skolkovo (few kilometers outside Moscow Ring Road). The building is accessible from Skolkovo Road (Сколковское шоссе) and Minskoe Highway (Минское шоссе).

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