Bounds for the sampling discretization error and their applications to the universal sampling discretization

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2025-05-05 DOI:10.1016/j.jco.2025.101958

E.D. Kosov , V.N. Temlyakov

引用次数: 0

Abstract

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 of sampling discretization of the

L_{p}

-norm on a given function class in terms of entropy numbers in the uniform norm of this class. As an example we apply these general results to obtain new error bounds for sampling discretization of the

L_{p}

-norms on classes of multivariate functions with mixed smoothness. In the second part of the paper we apply our general bounds to study the problem of universal sampling discretization.

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抽样离散误差的界限及其在通用抽样离散中的应用

本文第一部分研究了连续函数类的积分lp范数抽样离散化的绝对误差。我们用链技术的基本方法给出了给定函数类上的lp -范数抽样离散误差的一般上界，即该类一致范数中的熵数。作为一个例子，我们应用这些一般结果得到了混合光滑多变量函数类的lp -范数抽样离散化的新误差界。在论文的第二部分，我们应用我们的一般界来研究普遍抽样离散化问题。

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 Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.