Shape-preserving, multiscale fitting of univariate data by cubic L_1 smoothing splines

摘要

A new class of C~1 -smooth univariate cubic L_1 smoothing splines is introduced. The coefficients of these smoothing splines are calculated by minimizing the weighted sum of the t1 norm of the residuals of the data-fitting equations and the L ] norm of the second derivative of the spline. Cubic L_1 smoothing splines preserve shape well for arbitrary data, including multiscale data with abrupt changes in magnitude and spacing. Extensions to higher-degree and higher-dimensional smoothing splines are outlined.