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

Algorithms

Lu Yu¹  Qingwei Jin¹  John E. Lavery¹ 

[1]Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906, USA

[2] E-Mails:

关键词: antiderivative;    cubic L₁ spline;    first derivative;    5-point window;    function value;    global;    interpolation;    locally calculated;    second derivative;    univariate;   

DOI  :  10.3390/a3030311

来源: mdpi

【 摘 要 】

We compare univariate L₁ 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 the other types of L₁ splines. To calculate second-derivative-based 5-point-window L₁ splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm.

【 授权许可】

CC BY   
© 2010 by the authors; licensee MDPI, Basel, Switzerland.