Ivan Oseledets just mentioned the release of a newer algorithm within the TT-toolbox that performs a new Matrix/Tensor Factorization and he calls it the cross approximation From the page:
Cross approximation: introPosted on: 2014-02-26 00:00:00
the latest arxiv shows one use of it:Tensor trains
The basic operations with tensors in Tensor Train ( ) format have been implemented inBlock low-rank approximation techniques for large dense matrices
Fast multidimensional convolution in low-rank formats via cross approximation by M. V. Rakhuba, I. V. Oseledets
We propose a new cross-conv algorithm for approximate computation of convolution in different low-rank tensor formats (tensor train, Tucker, Hierarchical Tucker). It has better complexity with respect to the tensor rank than previous approaches. The new algorithm has a high potential impact in different applications. The key idea is based on applying cross approximation in the "frequency domain", where convolution becomes a simple elementwise product. We illustrate efficiency of our algorithm by computing the three-dimensional Newton potential and by presenting preliminary results for solution of the Hartree-Fock equation on tensor-product grids.
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