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MiS Preprint

On explicit QTT representation of Laplace operator and its inverse

Vladimir A. Kazeev and Boris N. Khoromskij


Ranks and explicit structure of some matrices in the Quantics Tensor Train format, which allows representation with logarithmic complexity in many cases, are investigated. The matrices under consideration are Laplace operator with various boundary conditions in D dimensions and inverse Laplace operator with Dirichlet and Dirichlet-Neumann boundary conditions in one dimension. The minimal-rank explicit QTT representations of these matrices presented are suitable for any high mode sizes and, in the multi-dimensional case, for any high dimensions.

MSC Codes:
15A69, 65F99
tensor decompositions, low-rank approximation, Quantics Tensor Train, QTT, inverse Laplace operator

Related publications

2012 Repository Open Access
Vladimir A. Kazeev and Boris N. Khoromskij

Low-Rank explicit QTT representation of the Laplace operator and inverse

In: SIAM journal on matrix analysis and applications, 33 (2012) 3, pp. 742-758