815 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- I. Oseledets26 · h 51
- A. Bogatyrev13 · h 10
- K. Metlov11 · h 14
- S. Matveev4 profiles10 · h 9
- A. Smirnov4 profiles8 · h 24
- M. Rakhuba2 profiles7 · h 6
- N. Brilliantov2 profiles6 · h 30
- P. Krapivsky2 profiles6 · h 45
- Alexander Osinsky2 profiles5 · h 12
- E. Tyrtyshnikov5 · h 32
- P. Berloff5 · h 33
- S. Budzinskiy5 · h 6
- Russian Academy of SciencesRU62 papers
- Skolkovo Institute of Science and TechnologyRU35 papers
- Lomonosov Moscow State UniversityRU22 papers
- Moscow Institute of Physics and TechnologyRU13 papers
- Donetsk Institute for Physics and Engineering named after O.O. GalkinUA7 papers
- Imperial College LondonGB6 papers
- Boston UniversityUS5 papers
- National Research University Higher School of EconomicsRU5 papers
- University of LeicesterGB5 papers
- University of HoustonUS4 papers
- University of ReadingGB4 papers
- ETH ZurichCH3 papers
39 papers · 1 filter
Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm
Stanislav Morozov, Dmitry Zheltkov, Alexander Osinsky
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitar…
Adaptive time-stepping for aggregation-shattering kinetics
Sergey A. Matveev, Viktor Zhilin, Alexander P. Smirnov
We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requ…
Estimates for the quantized tensor train ranks for the power functions
Sergey A. Matveev, Matvey Smirnov
In this work we provide theoretical estimates for the ranks of the power functions , in the quantized tensor train (QTT) format for $k = 1, 2, 3, \ldots, 2^{d}…
Nonnegative tensor train for the multicomponent Smoluchowski equation
Sergey A. Matveev, Ilya Tretyak
We propose an efficient implementation of the numerical tensor-train (TT) based algorithm solving the multicomponent coagulation equation preserving the nonnegativeness of solution…
Parametric Finite Element Discretization of the Surface Stokes Equations
Hanne Hardering, Simon Praetorius
We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which ar…
Exponential Euler and backward Euler methods for nonlinear heat conduction problems
M. A. Botchev, V. T. Zhukov
In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each…
Low-rank nonnegative tensor approximation via alternating projections and sketching
Azamat Sultonov, Sergey Matveev, Stanislav Budzinskiy
We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats. We use alternating projections between the nonnegative ortha…
Sketching for low-rank nonnegative matrix approximation: Numerical study
Sergey A. Matveev, Stanislav Budzinskiy
We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation o…
Tensor train completion: local recovery guarantees via Riemannian optimization
Stanislav Budzinskiy, Nikolai Zamarashkin
In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor tra…
Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics
A. Kalinov, A. I. Osinsky, S. A. Matveev +2
We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We t…
Tensor-Train Numerical Integration of Multivariate Functions with Singularities
Lev I. Vysotsky, Alexander V. Smirnov, Eugene E. Tyrtyshnikov
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth…
Model reduction in Smoluchowski-type equations
Ivan V. Timokhin, Sergey A. Matveev, Eugene E. Tyrtyshnikov +1
In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms.…
Verification benchmarks for single-phase flow in three-dimensional fractured porous media
Inga Berre, Wietse M. Boon, Bernd Flemisch +23
Flow in fractured porous media occurs in the earth's subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the…
Tensors in modelling multi-particle interactions
Daniil A. Stefonishin, Sergey A. Matveev, Dmitry A. Zheltkov
In this work we present recent results on application of low-rank tensor decompositions to modelling of aggregation kinetics taking into account multi-particle collisions (for thre…
Low-rank Riemannian eigensolver for high-dimensional Hamiltonians
Maxim Rakhuba, Alexander Novikov, Ivan Oseledets
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can b…
Modelling hidden structure of signals in group data analysis with modified (Lr, 1) and block-term decompositions
Pavel Kharyuk, Ivan Oseledets
This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tu…
Preconditioned Iterative Methods for Diffusion Problems with High-Contrast Inclusions
Yuliya Gorb, Vasiliy Kramarenko, Yuri Kuznetsov
This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear s…
Gradient Descent-based D-optimal Design for the Least-Squares Polynomial Approximation
V. P. Zankin, G. V. Ryzhakov, I. V. Oseledets
In this work, we propose a novel sampling method for Design of Experiments. This method allows to sample such input values of the parameters of a computational model for which the…
QTT-isogeometric solver in two dimensions
L. Markeeva, I. Tsybulin, I. Oseledets
The goal of this paper is to develop a numerical algorithm that solves a two-dimensional elliptic partial differential equation in a polygonal domain using tensor methods and ideas…
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
A. Cichocki, A-H. Phan, Q. Zhao +4
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-ord…
A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain
Alexander Lozovskiy, Maxim A. Olshanskii, Yuri V. Vassilevski
The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formu…
Probabilistic estimation of the rank 1 cross approximation accuracy
Alexander Osinsky
In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the…
Vico-Greengard-Ferrando quadratures in the tensor solver for integral equations
Valentin Khrulkov, Maxim Rakhuba, Ivan Oseledets
Convolution with Green's function of a differential operator appears in a lot of applications e.g. Lippmann-Schwinger integral equation. Algorithms for computing such are usually n…
Jacobi-Davidson method on low-rank matrix manifolds
Maxim Rakhuba, Ivan Oseledets
In this work we generalize the Jacobi-Davidson method to the case when eigenvector can be reshaped into a low-rank matrix. In this setting the proposed method inherits advantages o…