10 citations · 15 across the 6 of their papers we have counts for
7 papers
A single LU~factorization approach to model reduction for linear system families with a quadratic matrix pencil
Mikhail A. Botchev, Leonid Knizhnerman, Nikolai L. Zamarashkin +1
To solve a family of large linear systems where the system matrix depends on the family parameter quadratically, we propose a new solution approach. Our method employs the derivati…
Sufficient recovery conditions for noise-buried low rank tensors
Sergey Petrov, Nikolai Zamarashkin
Low-rank tensor approximation error bounds are proposed for the case of noisy input data that depend on low-rank representation type, rank and the dimensionality of the tensor. The…
On the optimal rank-1 approximation of matrices in the Chebyshev norm
Stanislav Morozov, Matvey Smirnov, Nikolai Zamarashkin
The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence…
Variational Bayesian inference for CP tensor completion with side information
Stanislav Budzinskiy, Nikolai Zamarashkin
We propose a message passing algorithm, based on variational Bayesian inference, for low-rank tensor completion with automatic rank determination in the canonical polyadic format w…
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 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…
Note: low-rank tensor train completion with side information based on Riemannian optimization
Stanislav Budzinskiy, Nikolai Zamarashkin
We consider the low-rank tensor train completion problem when additional side information is available in the form of subspaces that contain the mode- fiber spans. We propose an…