有限光滑加权Hermite空间中L2逼近和积分的可牵引性

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-10-01 DOI:10.1016/j.jco.2023.101768

Gunther Leobacher , Friedrich Pillichshammer , Adrian Ebert

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引用次数: 0

摘要

在本文中，我们考虑加权Hermite空间中Rs上函数的积分和L2近似。本文的第一部分致力于比较文献中出现的几个加权埃尔米特空间，这本身就很有趣。然后，我们研究了引入Hermite空间的积分和L2近似问题的可处理性，该问题描述了当误差阈值ε趋于0并且问题维数s增长到无穷大时信息复杂度的增长率。我们的主要结果是根据所涉及的权重来刻画可处理性，其对来自加权埃尔米特空间的函数的连续坐标方向的重要性进行了建模。

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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Tractability of L2-approximation and integration in weighted Hermite spaces of finite smoothness

In this paper we consider integration and $L_{2}$ -approximation for functions over $R^{s}$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of several weighted Hermite spaces that appear in literature, which is interesting on its own. Then we study tractability of the integration and $L_{2}$ -approximation problem for the introduced Hermite spaces, which describes the growth rate of the information complexity when the error threshold ε tends to 0 and the problem dimension s grows to infinity. Our main results are characterizations of tractability in terms of the involved weights, which model the importance of the successive coordinate directions for functions from the weighted Hermite spaces.

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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.