ON THE SPECTRAL PROPERTIES OF MATRICES ASSOCIATED WITH TREND FILTERS
研究了线性平滑器相关矩阵的谱性质，通过将平滑矩阵视为已知谱性质矩阵的扰动，推导了特征值和特征向量的解析结果，并用于近似特征分解以刻画平滑器性质。
This note is concerned with the spectral properties of matrices associated with linear smoothers. We derive analytical results on the eigenvalues and eigenvectors of smoothing matrices by interpreting the latter as perturbations of matrices belonging to algebras with known spectral properties, such as the circulant and the generalized tau. These results are used to characterize the properties of a smoother in terms of an approximate eigen-decomposition of the associated smoothing matrix.