Convolution via cross approximation

25/02/2014

Multidimensional convolution plays a crucial role in many applications. We have proposed a new method for approximate computation of the convolution in low-rank tensor formats that is based on the cross approximation in the frequency domain. The method is applicable to any SVD-based tensor format (skeleton, Tucker, Tensor Train, Hierachical Tucker). We have computed Newton potentials of different electronic densities, and also presented preliminary results for the solution of the Hartree-Fock equation on tensor product grids. For a practically interesting range of one-dimensional grid sizes \(n \sim 10^{3}-10^{5}\) our algorithm is faster.

He density H2 density

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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