21 citations · 41 across the 8 of their papers we have counts for
8 papers
On the algorithm of best approximation by low rank matrices in the Chebyshev norm
Stanislav Morozov, Nikolai Zamarashkin, Eugene Tyrtyshnikov
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of th…
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…
A residual concept for Krylov subspace evaluation of the matrix function
Mike A. Botchev, Leonid A. Knizhnerman, Eugene E. Tyrtyshnikov
An efficient Krylov subspace algorithm for computing actions of the matrix function for large matrices is proposed. This matrix function is widely used in exponential time inte…
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.…
Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma
S. V. Dolgov, A. P. Smirnov, E. E. Tyrtyshnikov
We consider the numerical modeling of the Farley-Buneman instability development in the earth's ionosphere plasma. The ion behavior is governed by the kinetic Landau equation in th…
Optimal rank matrix algebras preconditioners
F. Tudisco, C. Di Fiore, E. E. Tyrtyshnikov
When a linear system Ax = y is solved by means of iterative methods (mainly CG and GMRES) and the convergence rate is slow, one may consider a preconditioner P. The use of such pre…
Superfast solution of linear convolutional Volterra equations using QTT approximation
Jason A. Roberts, Dmitry V. Savostyanov, Eugene E. Tyrtyshnikov
We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices and the recently proposed…
Fast truncation of mode ranks for bilinear tensor operations
Dmitry Savostyanov, Eugene Tyrtyshnikov, Nikolay Zamarashkin
We propose a fast algorithm for mode rank truncation of the result of a bilinear operation on 3-tensors given in the Tucker or canonical form. If the arguments and the result have…