Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm

Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm

We compare univariateL1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that second-derivative-based 5-point-window L1 splines preserve shape as well as or better than...

Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows

We analytically investigate univariate C continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity and oscillation properties of the resulting L1 spline. These analytical results provide the basis for a computa...

Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines

Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms of second derivatives of the spline and the 1 norm of the residuals of the data-fitting equations. Cubic L1 smoothing splines are compared with conventional cubic smoothing splines based on the L2 and 2 norms. Computational results fo...

On Mixed Interpolating-Smoothing Splines and the ν-Spline

Time Registration Algorithm of Multi Sensors Based on Spline Interpolating

The time registration algorithm applicable to modern high-accuracy target tracking system is designed based on cubic spline interpolation. This algorithm can perform time registration for any quantity of sensors, the sensor measurement short of data, and the measurement of the sensor with non-uniform sampling period. The sampling rates obtained through registration can be selected according to ...