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

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

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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
- Application of the Principle of Adaptive Fourier Decomposition in Reproducing Kernel W₂ ¹[a,b] Space
- 广东工业大学学报 2021年38卷第3期页码：65-71
- 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：
  
  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
- 基金信息：
  
  广东省自然科学杰出青年基金资助项目(Yq2014060)
- DOI：10.12052/gdutxb.200094
  中图分类号： O242.2
- 网络首发：2021-05-10，
  
  纸质出版：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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