广东工业大学学报 ›› 2021, Vol. 38 ›› Issue (03): 65-71.doi: 10.12052/gdutxb.200094

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自适应Fourier分解思想在再生核W2 1 [a,b]空间的应用

蒋文超, 谭立辉   

  1. 广东工业大学 应用数学学院，广东 广州 510520
  • 收稿日期:2020-07-30 出版日期:2021-05-10 发布日期:2021-03-12
  • 作者简介:蒋文超(1995-)，女，硕士研究生，主要研究方向为自适应傅里叶分解在再生核空间的应用
  • 基金资助:
    广东省自然科学杰出青年基金资助项目(Yq2014060)

Application of the Principle of Adaptive Fourier Decomposition in Reproducing Kernel W2 1[a,b] Space

Jiang Wen-chao, Tan Li-hui   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2020-07-30 Online:2021-05-10 Published:2021-03-12

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摘要： 在再生核$W_2^1[a, b]$空间中研究自适应正交贪婪分解算法, 利用能量下降最快的原理自适应性地构造出最佳$n$项逼近函数, 并从理论上证明其收敛性成立。最后, 实验验证了在$W_2^1[a, b]$再生核空间中, 利用正交贪婪原理构造的$n$项数值原函数比用等分结点构造出的最佳$n$项数值原函数收敛效果更优。

关键词: 最佳数值原函数, 正交贪婪分解算法, 自适应Fourier分解, 数值逼近

Abstract: Te adaptive orthogonal greedy decomposition algorithm in the reproducing kernel $W_2^1[a, b]$-space is studied. The optimal n-term approximation function is adaptively constructed based on the principle of the fastest energy descent, and the convergence of this algorithm is proved theoretically. Finally, an experiment is used to verify that in the reproducing kernel $W_2^1[a, b]$-space, the best n-term numerical original function constructed by the orthogonal greedy principle has a better convergence effect than the best n-term numerical original function constructed with equal division nodes.

Key words: optimal numerical primitive function, orthogonal greedy algorithm, adaptive Fourier decomposition, numerical approximation

中图分类号: 

  • O242.2
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