815 citations · 3.2k across the 142 of their papers we have counts for
6 papers · 2 filters
Robust discretization in quantized tensor train format for elliptic problems in two dimensions
A. V. Chertkov, I. V. Oseledets, M. V. Rakhuba
In this work we propose an efficient black-box solver for two-dimensional stationary diffusion equations, which is based on a new robust discretization scheme. The idea is to formu…
Desingularization of bounded-rank matrix sets
Valentin Khrulkov, Ivan Oseledets
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and ex…
Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1
A. Cichocki, N. Lee, I. V. Oseledets +3
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently…
Calculating vibrational spectra of molecules using tensor train decomposition
Maxim Rakhuba, Ivan Oseledets
We propose a new algorithm for calculation of vibrational spectra of molecules using tensor train decomposition. Under the assumption that eigenfunctions lie on a low-parametric ma…
Convergence analysis of projected fixed-point iteration on a low-rank matrix manifold
Denis Kolesnikov, Ivan Oseledets
In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting sch…
"Compress and eliminate" solver for symmetric positive definite sparse matrices
Daria A. Sushnikova, Ivan V. Oseledets
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block…