混合光滑函数的数值加权积分

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-10-01 DOI:10.1016/j.jco.2023.101757

Dinh Dũng

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引用次数: 0

摘要

我们研究了混合光滑加权Sobolev空间中被积函数在Rd上的加权积分的逼近。对于来自这些空间的函数，我们证明了关于n个积分节点的最优象限的收敛速度的上界和下界。在一维情形（d=1）中，我们获得了最优象限的正确收敛速度。对于d≥2，上界由函数域Rd中阶跃双曲交叉上具有积分节点的稀疏网格象限执行。

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Numerical weighted integration of functions having mixed smoothness

We investigate the approximation of weighted integrals over $R^{d}$ for integrands from weighted Sobolev spaces of mixed smoothness. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to n integration nodes for functions from these spaces. In the one-dimensional case $(d = 1)$ , we obtain the right convergence rate of optimal quadratures. For $d \geq 2$ , the upper bound is performed by sparse-grid quadratures with integration nodes on step hyperbolic crosses in the function domain $R^{d}$ .

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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.