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Parameter choice strategies for regularized least squares approximation of noisy continuous functions on the unit circle (2403.19927v2)

Published 29 Mar 2024 in math.NA and cs.NA

Abstract: 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.

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