参数积分的随机复杂性和适应的作用 I. 有限维情况

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-12-27 DOI:10.1016/j.jco.2023.101821

Stefan Heinrich

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引用次数: 0

摘要

我们研究了向量估值均值计算的随机 n 次最小误差（以及复杂性），这是参数积分的离散版本。本文的结果构成了索博列夫空间中参数积分复杂性分析的基础，这将在第二部分中介绍。总之，本文扩展了海因里希和辛丹比韦（《复杂性》，15 (1999)，317-341）以及维根德（Shaker Verlag，2006 年）之前的研究成果。此外，我们还解决了基于信息的复杂性的一个基本问题，即随机设置中线性问题的适应能力。

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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Randomized complexity of parametric integration and the role of adaption I. Finite dimensional case

We study the randomized n-th minimal errors (and hence the complexity) of vector valued mean computation, which is the discrete version of parametric integration. The results of the present paper form the basis for the complexity analysis of parametric integration in Sobolev spaces, which will be presented in Part 2. Altogether this extends previous results of Heinrich and Sindambiwe (1999) [12] and Wiegand (2006) [27]. Moreover, a basic problem of Information-Based Complexity on the power of adaption for linear problems in the randomized setting is solved.

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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.