3 papers
math.NA2022
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…
math.NA2021
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…
math.NA2020
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…