经验插值方法与切比雪夫贪婪算法的新分析

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-04-22 DOI:10.1137/24m1634230

Yuwen Li

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引用次数: 0

摘要

SIAM数值分析杂志，第63卷，第2期，第931-948页，2025年4月。摘要。根据参数化函数类的熵值，给出了广义经验插值方法的收敛性估计。我们的分析是透明的，并且比通过Kolmogorov[数学]宽度的经典分析产生更快的收敛率。此外，我们还为目标函数的稀疏[数学]项非线性逼近导出了新的基于熵的Chebyshev贪婪算法的收敛估计。当相应的熵值衰减得足够快时，这也改进了经典的收敛分析。

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A New Analysis of Empirical Interpolation Methods and Chebyshev Greedy Algorithms

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 931-948, April 2025.
Abstract. We present new convergence estimates of generalized empirical interpolation methods in terms of the entropy numbers of the parametrized function class. Our analysis is transparent and leads to sharper convergence rates than the classical analysis via the Kolmogorov [math]-width. In addition, we also derive novel entropy-based convergence estimates of the Chebyshev greedy algorithm for sparse [math]-term nonlinear approximation of a target function. This also improves classical convergence analysis when corresponding entropy numbers decay fast enough.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.