Universal discretization and sparse recovery

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2025-05-13 DOI:10.1016/j.jat.2025.106199

F. Dai , V. Temlyakov

引用次数: 0

Abstract

Recently, it was discovered that for a given function class

F

the error of best linear recovery in the square norm can be bounded above by the Kolmogorov width of

F

in the uniform norm. That analysis is based on deep results in discretization of the square norm of functions from finite-dimensional subspaces. In this paper we show how very recent results on universal discretization of the square norm of functions from a collection of finite-dimensional subspaces lead to a Lebesgue-type inequality between the error of sparse recovery in the square norm provided by the algorithm based on least squares operator and best sparse approximations in the uniform norm with respect to appropriate dictionaries.

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通用离散化和稀疏恢复

最近，我们发现对于给定的函数类F，在平方范数中最佳线性恢复的误差可以以F在一致范数中的Kolmogorov宽度为界。该分析是基于有限维子空间中函数的平方范数离散化的深入结果。在本文中，我们展示了最近关于有限维子空间集合的函数的平方范数的普遍离散化的结果如何导致基于最小二乘算子的算法提供的平方范数的稀疏恢复误差与关于适当字典的均匀范数的最佳稀疏近似之间的lebesgue型不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.