Tensor properties of multilevel Toeplitz and related matrices

By Vadim Olshevsky, Ivan V. Oseledets, E. E. Tyrtyshnikov. 2006

54 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Computer Networks and Communications, Pure 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. Ivan V. Oseledets
3. Dmitry V. Savostyanov
4. Vladimir A. Kazeev
5. E. E. Tyrtyshnikov
6. Sergey V. Dolgov
7. Christine Tobler
8. Venera Khoromskaia

In Computational Theory and Mathematics

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

In Computer Networks and Communications

1. Boris N. Khoromskij
2. Vladimir A. Kazeev
3. E. E. Tyrtyshnikov
4. Dmitry V. Savostyanov
5. Ivan V. Oseledets

In Pure Mathematics

1. Boris N. Khoromskij
2. E. E. Tyrtyshnikov
3. Vladimir A. Kazeev
4. Dmitry V. Savostyanov
5. Ivan V. Oseledets

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “An early technique is based on best approximation in the Frobenius norm by a Kronecker product [251, 256], by a short sum of Kronecker products [203], or by a more general low-rank tensor decomposition.”
• Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity (2013, methodology): “CP structure of multilevel Toeplitz matrices related to that of generating vectors was presented in [18] and a general approach to fast algorithms for multilevel tensor-structured matrices in the CP format was considered in the same paper.”
• Tensor-Train Ranks for Matrices and Their Inverses (2011, background): “The blocks Ai1:sj1:s are referred to as blocks of the level s of A [11].”
• Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time (2008, methodology): “We can mention also some practical algorithms using interpolation and other function approximation techniques or additional structural properties rather than the given arrays of data [15, 22].”