univariate cubic l1 interpolating splines spline functional, window size and analysis-based algorithm单变量l1立方插值样条函数样条函数、窗口大小和分析算法.pdfVIP

Algorithms 2010, 3, 311-328; doi:10.3390/a3030311 OPEN ACCESS algorithms ISSN 1999-4893 /journal/algorithms Article Univariate Cubic Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm ,⋆ , Lu Yu , Qingwei Jin , John E. Lavery and Shu-Cherng Fang Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906, USA; E-Mails: qjin2@ (Q.J.); john.lavery2@ (J.L.); fang@ (S.-C.F.) Mathematical Sciences Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC 27709-2211, USA ⋆ Author to whom correspondence should be addressed; E-Mail: lyu@; Tel.: +01-919-513-1909; Fax: +01-919-515-5281. Received: 11 July 2010 / Accepted: 10 August 2010 / Published: 20 August 2010 Abstract: We compare univariate 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 splines preserve shape as well as or better than the other types of splines. To calculate second-derivative-based 5-point-window splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm. Keywords: anti