Abstract
This paper introduces a fully discrete soft thresholding trigonometric polynomial approximation on [−π,π], named Lasso trigonometric interpolation. This approximation is an ℓ1-regularized discrete least squares approximation under the same conditions of classical trigonometric interpolation on an equidistant grid. Lasso trigonometric interpolation is a sparse scheme which is efficient in dealing with noisy data. We theoretically analyze Lasso trigonometric interpolation quality for continuous periodic function. The L2 error bound of Lasso trigonometric interpolation is less than that of classical trigonometric interpolation, which improved the robustness of trigonometric interpolation. The performance of Lasso trigonometric interpolation for several testing functions (sin wave, triangular wave, sawtooth wave, square wave), is illustrated with numerical examples, with or without the presence of data errors.
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