自适应Fourier分解思想在再生核W2 1 [a,b]空间的应用

在再生核$W_2^1a, b]$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$W_2^1a, b]$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。

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

Te adaptive orthogonal greedy decomposition algorithm in the reproducing kernel $W_2^1a, b]$-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 $W_2^1a, b]$-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.