A new tensor decomposition

By Ivan V. Oseledets. 2009

53 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/1f5c26dac2cec97a7d0f5ab82997eb230f7ea6f1

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. Ivan V. Oseledets
3. Dmitry V. Savostyanov
4. Sergey V. Dolgov
5. E. E. Tyrtyshnikov
6. André Uschmajew
7. Christine Tobler
8. Vladimir A. Kazeev

In Computational Mechanics

1. Sergey V. Dolgov
2. Boris N. Khoromskij
3. Ivan V. Oseledets
4. Dmitry V. Savostyanov
5. André Uschmajew
6. E. E. Tyrtyshnikov
7. Nickolai L. Zamarashkin
8. Christine Tobler

Citations in the corpus

• Superfast Fourier Transform Using QTT Approximation (2012, background): “Statement 2 [39, 42] If unfoldings X { p } of a tensor X have ε p -ranks r p , then X can be approximated by the tensor ˜ X with TT-ranks r p and the following accuracy the word ‘car’ instead of the original ‘core’ [39, 42] to refer to components X (p) of (1), since the plural for ‘core’ is not…”
• Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation (2012, background): “It is therefore easily accessible and in principle applicable to more delicate types of redundancies as they, for instance, occur in the Tucker format or in the newly developed TT format [19, 20].”
• QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images (2012, background): “As shown in [10, 12, 13], QTT ranks are equal to the ranks of certain matricisations, i.”
• Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Für das TT Format wurde die Prozedur von Oseledets u. Tyrtyshnikov [75] bzw.”
• Tensor-Train Ranks for Matrices and Their Inverses (2011, methodology): “However, a recursive reduction of dimensionality naturally leads to tensor trains that proved to be most convenient for designing efficient algorithms (see [16, 19]).”
• Geometric Structures in Tensor Representations (Final Release) (2013, unknown): “The method has been reinvented by Oseledets and Tyrtyshnikov (see [28], [29], and [30]) and called ”TT decomposition”.”
• QTT approximation of elliptic solution operators in higher dimensions (2011, methodology): “The tensor-train (TT) decomposition [30, 31, 36] is free from the curse of dimensionality and can be computed by standard stable algorithms of linear algebra (SVD and QR decompositions).”