QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images

By Dmitry V. Savostyanov. 2012

13 citations recorded by the source corpus.

Subfields: Computational Mathematics, Electrical and Electronic Engineering, Hardware and Architecture

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Sergey V. Dolgov
2. Boris N. Khoromskij
3. Dmitry V. Savostyanov
4. Vladimir A. Kazeev
5. Ivan V. Oseledets
6. Christine Tobler
7. Venera Khoromskaia
8. V. Dolgov

In Electrical and Electronic Engineering

1. Boris N. Khoromskij
2. Vladimir A. Kazeev
3. Dmitry V. Savostyanov
4. Sergey V. Dolgov
5. Wolfgang Hackbusch
6. David J. Biagioni

In Hardware and Architecture

1. Sergey V. Dolgov
2. Vladimir A. Kazeev
3. Dmitry V. Savostyanov
4. Boris N. Khoromskij
5. Ivan V. Oseledets
6. Venera Khoromskaia
7. V. Dolgov
8. Lars Grasedyck

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “QTT has been applied to the solution of PDEs and eigenvalue problems [144, 154, 162], evaluation of boundary integrals in BEM [164], convolution [107] and the FFT [63, 108, 230].”
• Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse (2012, methodology): “For instance, the Fourier matrix is full-rank in the QTT format [6, Theorem 1], while the QTT ranks (exact or approximate) of Fourier images may be remarkably low [34, 6].”
• Superfast Fourier Transform Using QTT Approximation (2012, background): “This problem is solved for R = 1 ,ε = 0 (QTT-rank-one vectors with QTT-rank-one Fourier images) in [48].”