Parameter choice strategies for regularized least squares approximation of noisy continuous functions on the unit circle
<|reference_start|>Parameter choice strategies for regularized least squares approximation of noisy continuous functions on the unit circle: In this paper, we consider a trigonometric polynomial reconstruction of continuous periodic functions from their noisy values at equidistant nodes of the unit circle by a regularized least squares method. We indicate that the constructed trigonometric polynomial can be determined in explicit due to the exactness of trapezoidal rule. Then a concrete error bound is derived based on the estimation of Lebesgue constants. In particular, we analyze three regularization parameter choice strategies: Morozov's discrepancy principal, L-curve and generalized cross-validation. Finally, numerical examples are given to perform that well chosen parameters by above strategies can improve the quality of approximation significantly.<|reference_end|>
@article{an2024parameter,
    title={Parameter choice strategies for regularized least squares approximation
  of noisy continuous functions on the unit circle},
    author={Congpei An and Mou Cai},
    journal={arXiv preprint arXiv:2403.19927},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19927},
    primaryClass={math.NA cs.NA}
}