论文标题
套索三角学多项式近似，以定期函数恢复在等距点
Lasso trigonometric polynomial approximation for periodic function recovery in equidistant points
论文作者
论文摘要
在本文中，我们提出了$ [-π，π]上的完全离散的软阈值三角多项式近似，称为lasso三角插值。在等距网格上经典三角插值的相同条件下，此近似值是$ \ ell_1 $ regarlized离散的最小二乘近似。拉索三角插值很少，与此同时，它是处理嘈杂数据的有效工具。我们理论上分析了套索三角插值，以进行连续的周期性功能。主结果表明，$ l_2 $ lasso三角插值的误差限制小于经典三角插值的误差，这改善了三角插值的鲁棒性。本文还介绍了$ [-π，π] $上的Lasso三角插值的数值结果，无论是否存在数据误差。
In this paper, we propose a fully discrete soft thresholding trigonometric polynomial approximation on $[-π,π],$ 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 $[-π,π]$, with or without the presence of data errors.
