M. Nevskii

activity

20172023

most citedFive-dimensional Perfect Simplices

9 citations · 28 across the 9 of their papers we have counts for

collaborators

9 papers

math.MG2023

On a Geometric Approach to the Estimation of Interpolation Projectors

Mikhail Nevskii, Alexey Ukhalov

Suppose $Ω$ is a closed bounded subset of $R^{n},$ $S$ is an $n$ -dimensional non-degenerate simplex, $ξ (Ω; S) := min {σ \geq 1 : Ω \subset σ S}$ . Here $σ S$ is the…

math.MG2023★ 2 cited

The Minimum Norm of a Projector under Linear Interpolation on a Euclidean Ball

Mikhail Nevskii

We prove the following proposition. Under linear interpolation on a Euclidean $n$ -dimensional ball $B$ , an interpolation projector whose nodes coincide with the vertices of a regul…

math.MG2022★ 1 cited

On Some Estimate for the Norm of an Interpolation Projector

Mikhail Nevskii

Let $Q_{n} = [0, 1]^{n}$ be the unit cube in $R^{n}$ and let $C (Q_{n})$ be a space of continuous functions $f : Q_{n} \to R$ with the norm $\|f\|_{C(Q_n)}:=\max_{x\in Q_n}|f(x)|…

math.MG2021

Estimates for Interpolation Projectors and Related Problems in Computational Geometry

Mikhail Nevskii, Alexey Ukhalov

This paper contains a survey of results obtained by the authors mostly during the past few years and published by 2021. In particular, we present the best of known estimates of num…

math.MG2019★ 3 cited

Geometric Estimates in Interpolation by Linear Functions on a Euclidean Ball

Mikhail Nevskii

Let $B_{n}$ be the Euclidean unit ball in $R^{n}$ given by the inequality $∥ x ∥ \leq 1$ , $∥ x ∥ := (i = 1 \sum n x_{i}^{2})^{\frac{1}{2}}$ . By $C (B_{n})$ we mean th…

math.MG2019★ 9 cited

Interpolation by Linear Functions on an $n$ -Dimensional Ball

Mikhail Nevskii, Alexey Ukhalov

By $B = B (x^{(0)}; R)$ we denote the Euclidean ball in $R^{n}$ given by the inequality $∥ x - x^{(0)} ∥ \leq R$ . Here $x^{(0)} \in R^{n}, R > 0$ , $\|x\|:=\left(\sum_{i=1}^n x…

math.MG2019★ 4 cited

On Some Problems Related to a Simplex and a Ball

Mikhail Nevskii

Let $C$ be a convex body and let $S$ be a nondegenerate simplex in $R^{n}$ . Denote by $ξ (C; S)$ the minimal $τ > 0$ such that $C$ is a subset of the simplex $τ S$ . By $α (C; S)$ …

math.MG2018

Properties of 0/1-Matrices of Order n Having Maximum Determinant

Mikhail Nevskii, Alexey Ukhalov

We give some necessary conditions for maximality of $0/1$ -determinant. Let $M$ be a nondegenerate $0/1$ -matrix of order $n$ . Denote by $A$ the matrix of order $n + 1$ which…

math.MG2017★ 9 cited

Five-dimensional Perfect Simplices

Mikhail Nevskii, Alexey Ukhalov

Let $Q_{n} = [0, 1]^{n}$ be the unit cube in $R^{n}$ , $n \in N$ . For a nondegenerate simplex $S \subset R^{n}$ , consider the value $ξ(S)=\min \{σ>0: Q_n\subset σS\…

On a Geometric Approach to the Estimation of Interpolation Projectors

The Minimum Norm of a Projector under Linear Interpolation on a Euclidean Ball

On Some Estimate for the Norm of an Interpolation Projector

Estimates for Interpolation Projectors and Related Problems in Computational Geometry

Geometric Estimates in Interpolation by Linear Functions on a Euclidean Ball

Interpolation by Linear Functions on an n-Dimensional Ball

On Some Problems Related to a Simplex and a Ball

Properties of 0/1-Matrices of Order n Having Maximum Determinant

Five-dimensional Perfect Simplices

Interpolation by Linear Functions on an $n$ -Dimensional Ball