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

Jiang Wen-chao; Tan Li-hui

doi:10.12052/gdutxb.200094

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

更新时间：2026-05-27

- Application of the Principle of Adaptive Fourier Decomposition in Reproducing Kernel W₂ ¹[a,b] Space
- Vol. 38, Issue 3, Pages: 65-71(2021)
- 作者机构：
  
  广东工业大学应用数学学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.200094
  CLC： O242.2
- Online First：10 May 2021，
  
  Published：2021
- 稿件说明：
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蒋文超, 谭立辉. 自适应Fourier分解思想在再生核W₂ ¹ [a,b]空间的应用[J]. 广东工业大学学报, 2021, 38(3): 65-71. DOI: 10.12052/gdutxb.200094.

Jiang Wen-chao, Tan Li-hui. Application of the Principle of Adaptive Fourier Decomposition in Reproducing Kernel W₂ ¹[a,b] Space[J]. 2021, 38(3): 65-71. DOI: 10.12052/gdutxb.200094.
蒋文超, 谭立辉. 自适应Fourier分解思想在再生核W₂ ¹ [a,b]空间的应用[J]. 广东工业大学学报, 2021, 38(3): 65-71. DOI: 10.12052/gdutxb.200094. DOI：

Jiang Wen-chao, Tan Li-hui. Application of the Principle of Adaptive Fourier Decomposition in Reproducing Kernel W₂ ¹[a,b] Space[J]. 2021, 38(3): 65-71. DOI: 10.12052/gdutxb.200094. DOI：

摘要

在再生核

$W_2^1[a

b]$

img text_id='M3' class='formula-img' style='display:none;' src='gdgydxxb-38-3-65_M3.jpg'>

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

$n$

img text_id='M4' class='formula-img' style='display:none;' src='gdgydxxb-38-3-65_M4.jpg'>

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]$

img text_id='M3' class='formula-img' style='display:none;' src='gdgydxxb-38-3-65_M3.jpg'>

再生核空间中

利用正交贪婪原理构造的

$n$

img text_id='M4' class='formula-img' style='display:none;' src='gdgydxxb-38-3-65_M4.jpg'>

项数值原函数比用等分结点构造出的最佳

$n$

img text_id='M4' class='formula-img' style='display:none;' src='gdgydxxb-38-3-65_M4.jpg'>

项数值原函数收敛效果更优。

Abstract

Te adaptive orthogonal greedy decomposition algorithm in the reproducing kernel

$W_2^1[a

b]$

img text_id='M8' class='formula-img' style='display:none;' src='gdgydxxb-38-3-65_M8.jpg'>

-space is studied. The optimal

-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]$

img text_id='M8' class='formula-img' style='display:none;' src='gdgydxxb-38-3-65_M8.jpg'>

-space

the best

-term numerical original function constructed by the orthogonal greedy principle has a better convergence effect than the best

-term numerical original function constructed with equal division nodes.

关键词

Keywords

references

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