AFD Types Sparse Representations vs. the Karhunen-Loeve Expansion for Decomposing Stochastic Processes

@article{Qian2022AFDTS,
  title={AFD Types Sparse Representations vs. the Karhunen-Loeve Expansion for Decomposing Stochastic Processes},
  author={Tao Qian and Wei Qu},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.00844}
}
A BSTRACT . This article introduces adaptive Fourier decomposition (AFD) type methods, emphasizing on those that can be applied to stochastic processes and random fields, mainly including stochastic adaptive Fourier decomposition and stochastic pre-orthogonal adaptive Fourier decomposition. We establish their algorithms based on the covariant function and prove that they enjoy the same convergence rate as the Karhunen-Lo`eve (KL) decomposition. The AFD type methods are compared with the KL… 

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