Journal of Guangdong University of Technology ›› 2021, Vol. 38 ›› Issue (03): 65-71.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

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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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

CLC Number: 

  • O242.2
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