The minimal radius of Galerkin information for the problem of numerical differentiation

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-08-05 DOI:10.1016/j.jco.2023.101787

S.G. Solodky, S.A. Stasyuk

引用次数: 0

Abstract

The problem of numerical differentiation for periodic functions with finite smoothness is investigated. For multivariate functions, different variants of the truncation method are constructed and their approximation properties are obtained. Based on these results, sharp bounds (in the power scale) of the minimal radius of Galerkin information for the problem under study are found.

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数值微分问题的伽辽金信息的最小半径

研究了有限光滑周期函数的数值微分问题。对于多元函数，构造了截断法的不同变体，并得到了它们的近似性质。基于这些结果，找到了所研究问题的伽辽金信息最小半径的明确界(在幂标度上)。

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.