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Mathematics > Numerical Analysis

arXiv:2210.04204 (math)
[Submitted on 9 Oct 2022 (v1), last revised 21 Sep 2023 (this version, v4)]

Title:Lasso trigonometric polynomial approximation for periodic function recovery in equidistant points

Authors:Congpei An, Mou Cai
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Abstract:In this paper, we propose a fully discrete soft thresholding trigonometric polynomial approximation on $[-\pi,\pi],$ named Lasso trigonometric interpolation. This approximation is an $\ell_1$-regularized discrete least squares approximation under the same conditions of classical trigonometric interpolation on an equidistant grid. Lasso trigonometric interpolation is sparse and meanwhile it is an efficient tool to deal with noisy data. We theoretically analyze Lasso trigonometric interpolation for continuous periodic function. The principal results show that the $L_2$ error bound of Lasso trigonometric interpolation is less than that of classical trigonometric interpolation, which improved the robustness of trigonometric interpolation. This paper also presents numerical results on Lasso trigonometric interpolation on $[-\pi,\pi]$, with or without the presence of data errors.
Comments: 18 pages, 5 figures
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2210.04204 [math.NA]
  (or arXiv:2210.04204v4 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2210.04204

Submission history

From: Mou Cai [view email]
[v1] Sun, 9 Oct 2022 09:12:05 UTC (1,081 KB)
[v2] Mon, 17 Oct 2022 18:06:30 UTC (1,179 KB)
[v3] Sun, 23 Apr 2023 12:24:05 UTC (1,657 KB)
[v4] Thu, 21 Sep 2023 17:01:32 UTC (1,502 KB)
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