Zobrazeno 1 - 10
of 429
pro vyhledávání: '"A. A. Temlyakov"'
Autor:
Gasnikov, A., Temlyakov, V.
The general theory of greedy approximation with respect to arbitrary dictionaries is well developed in the case of real Banach spaces. Recently, some of results proved for the Weak Chebyshev Greedy Algorithm (WCGA) in the case of real Banach spaces w
Externí odkaz:
http://arxiv.org/abs/2408.03214
Although the basic idea behind the concept of a greedy basis had been around for some time, the formal development of a theory of greedy bases was initiated in 1999 with the publication of the article [S.~V.~Konyagin and V.~N.~Temlyakov, A remark on
Externí odkaz:
http://arxiv.org/abs/2405.20939
Recently, in a number of papers it was understood that results on sampling discretization and on the universal sampling discretization can be successfully used in the problem of sampling recovery. Moreover, it turns out that it is sufficient to only
Externí odkaz:
http://arxiv.org/abs/2402.00848
Autor:
Kosov, E. D., Temlyakov, V. N.
In the first part of the paper we study absolute error of sampling discretization of the integral $L_p$-norm for function classes of continuous functions. We use basic approaches from chaining technique to provide general upper bounds for the error o
Externí odkaz:
http://arxiv.org/abs/2312.05670
Autor:
Dai, F., Temlyakov, V.
Recently, it has been discovered that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error being measured in the square norm. It was established that a simple greedy type algorithm -- Weak
Externí odkaz:
http://arxiv.org/abs/2307.04161
Autor:
Kosov, E. D., Temlyakov, V. N.
Publikováno v:
Journal of Mathematical Analysis and Applications, 538(2), 2024, 128431
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is sufficient to us
Externí odkaz:
http://arxiv.org/abs/2306.14207
Autor:
Dai, F., Temlyakov, V.
Publikováno v:
J. Math. Anal. Appl., Vol 529,2024, No. 1, Paper No. 127570, 28
There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling discretization
Externí odkaz:
http://arxiv.org/abs/2301.12536
Autor:
Dai, F., Temlyakov, V.
Recently, it was discovered that for a given function class $\mathbf{F}$ the error of best linear recovery in the square norm can be bounded above by the Kolmogorov width of $\mathbf{F}$ in the uniform norm. That analysis is based on deep results in
Externí odkaz:
http://arxiv.org/abs/2301.05962
Publikováno v:
Journal of Functional Analysis 2023
The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of the Nikol's
Externí odkaz:
http://arxiv.org/abs/2208.09762
A set $Q$ in $\mathbb{Z}_+^d$ is a lower set if $(k_1,\dots,k_d)\in Q$ implies $(l_1,\dots,l_d)\in Q$ whenever $0\le l_i\le k_i$ for all $i$. We derive new and refine known results regarding the cardinality of the lower sets of size $n$ in $\mathbb{Z
Externí odkaz:
http://arxiv.org/abs/2208.02113