Sparse Numerical Approximation Of Adaptive Fourier Decomposition In Reproducing Kernel Space W₂¹[a,b]

Since the 21st century,with the widely use of computers and communication equipment,the data has also increased geometrically.In order to better fit the data,this paper studies the adaptive orthogonal greedy decomposition algorithm in the reproducing kernel spaceW₂¹[a,b],and use the principle of energy decreased fastest adaptively to construct the best n term approximation function,and proves its convergence theoretically.Then,a numerical experiment is used to verify that in the regenerated kernel spaceW₂¹[a,b],the optimal numerical original function constructed by the principle of orthogonal greedy decomposition has better convergence than the construction with equal division nodes.In order to solve the noise interference and over-fitting phenomenon of the data,we further considered the adaptive Fourier algorithm corresponding to the Tikhonov regularization kernel in spaceW₂¹[a,b],discussed the error analysis and convergence bounds of its approximation function,and finally used the experiment to demonstrate that improved algorithm can fit the noise data effectively.The relevant conclusions of this paper can also be used as the basic theory of numerical application to be extended to other reproducing kernel spaces and to realize the application of sparse numerical solution of differential equations and integral equations.