Tensorisation of vectors and their efficient convolution

By Wolfgang Hackbusch. 2011

61 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics

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

In Computational Theory and Mathematics

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

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 [145, 155, 163, 188], evaluation of boundary integrals in BEM [165], convolution [108] and the FFT [64, 109, 231].”
• Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity (2013, background): “Algebraic view of convolution of tensorized vectors in the Hierarchical Tucker format was presented in [41].”
• Superfast Fourier Transform Using QTT Approximation (2012, methodology): “There are more examples of high-dimensional problems which were efficiently solved using the QTT approximation [4, 36, 37] as well as H -Tucker format [15].”
• Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances (2012, methodology): “Direct convolution transform of N -d tensors in O(d logN) operations using the explicit QTT representation of multilevel Toeplitz matrices is developed in [46] (see also the discussion in [31]).”