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Date
2010Type
- Report
ETH Bibliography
yes
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Abstract
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. Show more
Publication status
unpublishedJournal / series
Preprint / Max-Planck-InstitutVolume
Publisher
Max-Planck-Institut für Mathematik in den NaturwissenschaftenSubject
Tensor decompositions; Low-rank approximation; Quantics Tensor Train; QTT; Inverse Laplace operatorOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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ETH Bibliography
yes
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