New tensor decomposition
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, andÂ the results for the computation of the smallest eigenvalue of a 19-dimensional operator are presented.