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...ike canonical, Tucker and matrix 2 product states (or tensor train) representations, as well as basics of multilinear algebra and the recent tensor numerical methods for solving PDEs, can be found in =-=[34, 32, 17, 33]-=- (see also Dissertations [22] and [11]). The presented approach yields enormous reduction in storage and computing time. Our numerical results show that summation of two millions of potentials on a 3D...

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...ured representation of the discrete problem to extract the effective degrees of freedom adaptively and make the problem tractable. A broad overview of this methodology can be seen in recent surveys =-=[33, 17, 16, 29]-=-. This tensor approach was first applied to parametric and stochastic PDEs in [24] based on the canonical format and it was further extended in [34, 32, 13] to the case of Hierarchical Tucker, as well...

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...urposes, we proceed to first give a simplified presentation of the TT decomposition for three independent variables. A detailed discussion on TT decomposition can be found in recent surveys and books =-=[19, 18, 25]-=-. 5.1 Tensor Train decomposition The first operation we need for high-dimensional data is reshaping. To this end, suppose y is the solution of (20). Its elements can be naturally enumerated by three i...

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...ike canonical, Tucker and matrix 2 product states (or tensor train) representations, as well as basics of multilinear algebra and the recent tensor numerical methods for solving PDEs, can be found in =-=[34, 32, 17, 33]-=- (see also Dissertations [22] and [11]). The presented approach yields enormous reduction in storage and computing time. Our numerical results show that summation of two millions of potentials on a 3D...