Approximation of matrices with logarithmic number of parameters

By Ivan V. Oseledets. 2009

73 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f15fa63596aa426e742a187135fa1028f9d2112c

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

1. Boris N. Khoromskij
2. Vladimir A. Kazeev
3. Ivan V. Oseledets
4. E. E. Tyrtyshnikov
5. Christoph Schwab
6. Dmitry V. Savostyanov
7. Oleg Reichmann
8. Wolfgang Hackbusch

In Computational Mathematics

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

In Computational Theory and Mathematics

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

Citations in the corpus

• Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse (2012, methodology): “Also, one may adopt the quantized tensor train (QTT) format [30, 19, 31], which is the TT format applied to a vector after virtual dimensions are introduced by reshaping it to smaller mode sizes (for example, nk = 2).”
• QTT approximation of elliptic solution operators in higher dimensions (2011, methodology): “The numerical algorithms are based on the idea of truncated preconditioned iteration [15, 19, 21] via the TT-approximation method [30, 36], combined with the quantics reshaping of arising multidimensional arrays [21, 32, 33].”
• Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity (2013, methodology): “In order to make it sublinear, one may adopt the QTT format [6, 7, 8], which is the particular case of the TT format with the smallest possible mode sizes, applied to tensors reshaped correspondingly.”
• Constructive Representation of Functions in Low-Rank Tensor Formats (2012, methodology): “QTT was introduced in [26, 28] in the context of tensorization of matrices and then studied by Khoromskij [21] for vectors, where it was shown that for the corresponding tensor has canonical rank 1 (thus, all TT-ranks are equal to 1), and for the function the TT-ranks are equal to 2.”
• Low-rank tensor structure of linear diffusion operators in the TT and QTT formats☆ (2013, methodology): “With the aim of further reduction of the complexity, the TT format can be applied to a “quantized” vector (matrix), which leads to the Quantized Tensor Train (QTT) format [15, 16, 17].”