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- Ivan V. Oseledets
- SIAM J. Scientific Computing
- 2011

A simple nonrecursive form of the tensor decomposition in d dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number ofâ€¦ (More)

We propose a simple two-step approach for speeding up convolution layers within large convolutional neural networks based on tensor decomposition and discriminative fine-tuning. Given a layer, we useâ€¦ (More)

Article history: Received 19 July 2009 Accepted 27 July 2009 Available online 21 August 2009 Submitted by V. Sergeichuk AMS classification: 15A12 65F10 65F15

- Ivan V. Oseledets, Eugene E. Tyrtyshnikov
- SIAM J. Scientific Computing
- 2009

For d-dimensional tensors with possibly large d > 3, an hierarchical data structure, called the Tree-Tucker format, is presented as an alternative to the canonical decomposition. It hasâ€¦ (More)

- Ivan V. Oseledets, S. V. Dolgov
- SIAM J. Scientific Computing
- 2012

Tensors arise naturally in high-dimensional problems in chemistry, financial mathematics and many others. The numerical treatment of such kind of problems is difficult due to the curse ofâ€¦ (More)

- Ivan V. Oseledets
- SIAM J. Matrix Analysis Applications
- 2010

- S. V. Dolgov, Boris N. Khoromskij, Ivan V. Oseledets, Dmitry V. Savostyanov
- Computer Physics Communications
- 2014

We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from highâ€“dimensional problems. We use the tensor train format (TT) for vectors andâ€¦ (More)

- Dmitry V. Savostyanov, Ivan V. Oseledets
- The 2011 International Workshop onâ€¦
- 2011

Using recently proposed tensor train format for the representation of multi-dimensional dense arrays (tensors) we develop a fast interpolation method to approximate the given tensor by using only aâ€¦ (More)

- Boris N. Khoromskij, Ivan V. Oseledets
- Comput. Meth. in Appl. Math.
- 2010

We investigate the convergence rate of QTT stochastic collocation tensor approximations to solutions of multi-parametric elliptic PDEs, and construct efficient iterative methods for solving arisingâ€¦ (More)

- Pierre-Antoine Absil, Ivan V. Oseledets
- Comp. Opt. and Appl.
- 2015

Retractions are a prevalent tool in Riemannian optimization that provides a way to smoothly select a curve on a manifold with given initial position and velocity. We review and propose severalâ€¦ (More)