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Fast multidimensional convolution in low-rank formats via cross approximation

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 نشر من قبل Maxim Rakhuba
 تاريخ النشر 2014
  مجال البحث
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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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