New tensor decomposition

15/03/2009

A new paper, A compact matrix form of the d-dimensional tensor decomposition is added. A new version of the TT (name is now not coming from “Tree Tucker”, but from “Three dimensional Tensors” which are the defining parameters of the format) format is presented, which is much simpler than the recursive TT format and the subspace format by Hackbusch and Kuhn (they do not present any numerical experiments). It presents a nice and clear way to implement basic operations, like matrix-by-vector product, multidimensional convolution, norms, and what is the most important, the recompression procedure is based entirely on the SVD and QR decompositions. Its implementation takes about 150 lines of Matlab code compared to thousand of lines for the recursive TT-format, and  the results for the computation of the smallest eigenvalue of a 19-dimensional operator are presented.

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

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