Y. Malykhin

activity

20162026

most citedProduct of octahedra is badly approximated in the

ℓ_{2, 1}

-metric

2 citations · 3 across the 9 of their papers we have counts for

collaborators

10 papers

math.NA2026

Some theoretical and practical results on noisy signals recovery

M. Makurin, Yu. Malykhin, K. Ryutin +1

We discuss some theoretical results and their applications to specific practical problems from wireless communications. We assume that we know the noisy version of the signal, whic…

math.FA2026

Rigidity of sets of independent functions in symmetric spaces

Sergey V. Astashkin, Yu. V. Malykhin

We say that a symmetric function space $X$ has the $(I R)$ property whenever all sets of $N$ independent mean zero functions $f_{1}, \dots, f_{N} \in X$ , $∥ f_{k} ∥_{X} \geq 1$ , are poorly appr…

math.FA2025

Kolmogorov widths of the class $W_{1}^{1}$

Yuri Malykhin

We prove that $d_{n} (W_{1}^{1}, L_{q}) ≍ n^{- 1/2} lo g n$ , $2 < q < \infty$ . This completes the study of orders of decay of Kolmogorov widths for the classical case of the univariate Sobolev…

math.FA2023

Polynomial approximation on disjoint segments and amplification of approximation

Yuri Malykhin, Konstantin Ryutin

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem ha…

math.FA2022

Widths and rigidity

Yuri Malykhin

We consider Kolmogorov widths of finite sets of functions. Any orthonormal system of $N$ functions is rigid in $L_{2}$ , i.e. it cannot be well approximated by linear subspaces of dim…

math.MG2021

Search of fractal space-filling curves with minimal dilation

Yuri Malykhin, Evgeny Shchepin

We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers~ -- heuristic algorithms that find models for CNF boolean form…

math.FA2021

Recovery of regular ridge functions on the ball

Tatyana Zaitseva, Yuri Malykhin, Konstantin Ryutin

We consider the problem of the uniform (in $L_{\infty}$ ) recovery of ridge functions $f (x) = φ (⟨ a, x ⟩)$ , $x \in B_{2}^{n}$ , using noisy evaluations $y_1\approx f(x^1),\ldots,y_N…

math.FA2020

Kolmogorov widths of Besov classes $B_{1, θ}^{1}$ and products of octahedra

Yuri Malykhin

In this paper we find the orders of decay for Kolmogorov widths of some Besov classes related to $W_{1}^{1}$ (the behaviour of the widths for $W_{1}^{1}$ remains unknown): $$ d_n(B^1_{1,θ}…

math.FA2020★ 1 cited

Matrix and tensor rigidity and $L_{p}$ -approximation

Yuri Malykhin

In this paper we apply methods originated in Complexity theory to some problems of Approximation. We notice that the construction of Alman and Williams that disproves the rigidity…

math.FA2016★ 2 cited

Product of octahedra is badly approximated in the $ℓ_{2, 1}$ -metric

Yu. V. Malykhin, K. S. Ryutin

We prove that the cartesian product of octahedra $B_{1, \infty}^{n, m} = B_{1}^{n} \times \dots \times B_{1}^{n}$ ( $m$ octahedra) is badly approximated by half--dimensional subspaces in mixed--n…

Some theoretical and practical results on noisy signals recovery

Rigidity of sets of independent functions in symmetric spaces

Kolmogorov widths of the class W11​

Polynomial approximation on disjoint segments and amplification of approximation

Widths and rigidity

Search of fractal space-filling curves with minimal dilation

Recovery of regular ridge functions on the ball

Kolmogorov widths of Besov classes B1,θ1​ and products of octahedra

Matrix and tensor rigidity and Lp​-approximation

Product of octahedra is badly approximated in the ℓ2,1​-metric

Kolmogorov widths of the class $W_{1}^{1}$

Kolmogorov widths of Besov classes $B_{1, θ}^{1}$ and products of octahedra

Matrix and tensor rigidity and $L_{p}$ -approximation

Product of octahedra is badly approximated in the $ℓ_{2, 1}$ -metric