Tractability results for integration in subspaces of the Wiener algebra

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2025-04-16 DOI:10.1016/j.jco.2025.101948

Josef Dick , Takashi Goda , Kosuke Suzuki

引用次数: 0

Abstract

In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the d-dimensional unit cube. We show that intractability holds for multivariate integration in the standard Wiener algebra in the deterministic setting, in contrast to polynomial tractability in an unweighted subspace of the Wiener algebra recently shown by Goda (2023). Moreover, we prove that multivariate integration in the subspace of the Wiener algebra introduced by Goda is strongly polynomially tractable if we switch to the randomized setting, where we obtain a better ε-exponent than the one implied by the standard Monte Carlo method. We also identify subspaces in which multivariate integration in the deterministic setting are (strongly) polynomially tractable and we compare these results with the bound which can be obtained via Hoeffding's inequality.

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维纳代数子空间积分的可溯性结果

在本文中，我们提出了与 d 维单位立方体上的维纳代数子空间中的积分问题有关的一些新（不）可操作性结果。我们证明，在确定性环境中，标准维纳代数中的多元积分问题是难以解决的，这与戈达（2023）最近证明的维纳代数非加权子空间中的多项式可计算性截然不同。此外，我们还证明，如果切换到随机设置，戈达引入的维纳代数子空间中的多变量积分具有很强的多项式可操作性，在随机设置中，我们得到的ε指数比标准蒙特卡罗方法隐含的指数更好。我们还确定了确定性设置中多元积分（强）多项式可控的子空间，并将这些结果与通过霍夫定不等式得到的约束进行了比较。

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.